Burton impressed as they began life in the Football League, but were defeated by last year's play-off finalists.
New goalkeeper Shane Redmond should have prevented two Shrewsbury goals - Jake Robinson beating him from a tight angle with 10 minutes gone.
Joss Labadie's 30-yard free-kick squirmed past Redmond late on, after Dave Hibbert's header had made it two.
Burton sub Greg Pearson had pulled one back with a fierce shot, and also hit the bar, before Labadie made sure.
Shrewsbury boss Paul Simpson told BBC Radio Shropshire:
"It's the three points you want to start the season.
"We can still get better - remember, there were a lot of changes out there.
"And Dave Hibbert was a really late call-up when we found we didn't have clearance from the Greek FA for Kris Bright. Dave ran his socks off, and scored a fantastic goal."
Burton Albion boss Paul Peschisolido told BBC Radio Derby: "We started sloppy right from the kick-off and before we knew it we were a goal down.
"But we picked ourselves up, kept possession and created two or three chances but it just didn't happen in the first half.
"Again we conceded a sloppy goal in the second half but after that we played some good stuff.
"But there's no point in sitting here crying, we have to get on with it. The season's not won and lost in the first game of the season."
90:00+3:35 The final whistle is blown by the referee.
90:00+2:22 Jake Simpson takes a short corner, clearance by Paul Boertien.
90:00+2:02 Short corner taken by Jake Simpson, clearance made by Guy Branston.
Correction - 90:00+1:01 Short corner taken by Jake Simpson, Paul Murray takes a shot. Save by Shane Redmond.
90:00+1:01 Jake Simpson decides to take the corner short, Paul Murray takes a shot. Save by Shane Redmond.
90:00+0:32 Joss Labadie takes the outswinging corner, Paul Murray takes a shot. Save made by Shane Redmond.
90:00+0:21 Jake Simpson produces a cross, Marc Edworthy manages to make a clearance.
88:47 Substitution Andre Gray on for Nathan Elder.
88:07 Paul Murray challenges Russell Penn unfairly and gives away a free kick. Free kick taken by Marc Edworthy.
87:34 Shot from just outside the box by Omer Riza misses to the right of the goal.
86:41 Corner taken right-footed by Joss Labadie from the left by-line, Ryan Austin manages to make a clearance.
86:19 Inswinging corner taken by Joss Labadie from the left by-line, Marc Edworthy manages to make a clearance.
86:03 The assistant referee flags for offside against Darren Stride. Chris Neal takes the free kick.
84:20 Greg Pearson has an effort at goal from the edge of the area that misses to the right of the target.
83:41 Shot from just outside the box by Ryan Austin misses to the right of the target.
83:02 Unfair challenge on Guy Branston by Omer Riza results in a free kick. Indirect free kick taken by Shane Redmond.
82:32 Substitution (Shrewsbury) makes a substitution, with Omer Riza coming on for Jake Robinson.
82:05 GOAL - Joss Labadie:Shrewsbury 3 - 1 Burton Albion Joss Labadie scores a goal direct from the free kick from just outside the penalty area to the bottom left corner of the goal. Shrewsbury 3-1 Burton Albion.
80:24 Booking Guy Branston receives a caution for unsporting behaviour.
Correction - 80:13 Free kick awarded for a foul by Guy Branston on Nathan Elder.
80:13 Unfair challenge on Nathan Elder by Guy Branston results in a free kick. Free kick taken by Joss Labadie.
79:26 Substitution Darren Stride comes on in place of Jimmy Phillips.
78:25 Kevin McIntyre challenges Greg Pearson unfairly and gives away a free kick. John McGrath takes the indirect free kick.
76:41 Inswinging corner taken by John McGrath from the right by-line played to the near post.
76:11 Free kick awarded for an unfair challenge on Guy Branston by Nathan Elder. Paul Boertien restarts play with the free kick.
72:41 Outswinging corner taken right-footed by Joss Labadie, clearance made by Guy Branston.
72:33 The ball is swung over by Jake Simpson, Ryan Austin manages to make a clearance.
71:57 Joss Labadie concedes a free kick for a foul on Russell Penn. Free kick taken by Shane Redmond.
70:58 Richard Walker is ruled offside. Chris Neal takes the indirect free kick.
70:25 Craig Disley handles the ball and concedes a free kick. Ryan Austin takes the free kick.
69:33 Kevin McIntyre fouled by Greg Pearson, the ref awards a free kick. Chris Neal takes the free kick.
68:37 A cross is delivered by Ryan Austin, Greg Pearson takes a shot. Save by Chris Neal.
67:36 Inswinging corner taken by Jimmy Phillips from the right by-line, clearance by Joss Labadie.
67:12 Greg Pearson takes a shot. Save by Chris Neal.
65:46 Inswinging corner taken from the left by-line by Jake Simpson, clearance by Guy Branston.
63:42 Inswinging corner taken by John McGrath from the right by-line played to the near post, Strike from close range by Richard Walker clears the bar.
63:24 Jacques Maghoma produces a cross, Joss Labadie manages to make a clearance.
61:18 Assist by Russell Penn.
61:18 GOAL - Greg Pearson:Shrewsbury 2 - 1 Burton Albion Greg Pearson scores a goal from deep inside the penalty area low into the middle of the goal. Shrewsbury 2-1 Burton Albion.
60:07 Shot from just outside the penalty box by Nathan Elder misses to the left of the target.
59:24 Centre by Greg Pearson, save by Chris Neal.
58:46 The ball is swung over by Jake Simpson.
58:21 Unfair challenge on Greg Pearson by Kelvin Langmead results in a free kick. Richard Walker takes the free kick.
57:50 The offside flag is raised against Kevin McIntyre. Free kick taken by Shane Redmond.
56:51 Substitution Dave Hibbert goes off and Jake Simpson comes on.
56:19 Substitution Greg Pearson joins the action as a substitute, replacing Robin Shroot.
54:42 Graham Coughlan fouled by Richard Walker, the ref awards a free kick. Chris Neal takes the indirect free kick.
53:25 The ball is crossed by Jacques Maghoma, Craig Disley fouled by Jimmy Phillips, the ref awards a free kick. Free kick taken by Chris Neal.
51:15 Free kick awarded for a foul by Nathan Elder on John McGrath. Free kick taken by Ryan Austin.
49:59 John McGrath has shot on goal from just outside the penalty box which goes wide of the right-hand upright.
48:54 Assist on the goal came from Kevin McIntyre.
48:54 GOAL - Dave Hibbert:Shrewsbury 2 - 0 Burton Albion Dave Hibbert finds the back of the net with a goal from inside the six-yard box to the top left corner of the goal. Shrewsbury 2-0 Burton Albion.
48:18 Short corner taken by Joss Labadie,
47:51 Centre by Guy Branston.
45:17 Graham Coughlan challenges Robin Shroot unfairly and gives away a free kick. Strike comes in from Ryan Austin from the free kick, Dave Hibbert gets a block in.
45:01 The game restarts for the second half.
Half Time
45:00+2:51 The referee blows for half time.
45:00+1:31 Foul by Kelvin Langmead on Robin Shroot, free kick awarded. Shot on goal comes in from Jacques Maghoma from the free kick, save by Chris Neal.
45:00+0:35 John McGrath takes a shot. Chris Neal makes a save.
44:33 A cross is delivered by Dean Holden, Shane Redmond makes a clearance.
43:29 Jimmy Phillips sends in a cross, Joss Labadie makes a clearance.
Correction - 42:58 Short corner taken by Dean Holden. Jimmy Phillips crosses the ball,
42:58 Short corner taken by Dean Holden. The ball is sent over by Jimmy Phillips,
42:51 A cross is delivered by Robin Shroot, Kelvin Langmead manages to make a clearance.
41:31 A cross is delivered by Paul Murray.
41:03 Paul Boertien challenges Dave Hibbert unfairly and gives away a free kick. Indirect free kick taken by Dean Holden.
40:33 Unfair challenge on Paul Boertien by Nathan Elder results in a free kick. Paul Boertien takes the free kick.
38:58 Free kick awarded for a foul by Joss Labadie on Russell Penn. Shane Redmond takes the indirect free kick.
38:50 Dean Holden crosses the ball, clearance by Guy Branston.
37:59 Shot from just outside the box by Jimmy Phillips goes over the crossbar.
37:50 Jacques Maghoma sends in a cross, Chris Neal makes a save.
37:03 Nathan Elder produces a cross, save made by Shane Redmond.
36:12 Jimmy Phillips takes a shot. Dean Holden gets a block in.
35:36 Craig Disley takes a shot. Paul Boertien gets a block in.
35:11 Unfair challenge on Joss Labadie by Jimmy Phillips results in a free kick. Free kick taken by Graham Coughlan.
34:15 Jimmy Phillips fouled by Paul Murray, the ref awards a free kick. Free kick taken by Paul Boertien.
33:46 Jacques Maghoma produces a cross, save made by Chris Neal.
32:54 The ball is sent over by Paul Murray, Guy Branston manages to make a clearance.
31:48 The ball is delivered by Craig Disley, Dave Hibbert takes a shot. Save by Shane Redmond. Outswinging corner taken by Joss Labadie from the right by-line, Ryan Austin manages to make a clearance.
30:20 Jacques Maghoma sends in a cross, Effort on goal by Jimmy Phillips from just outside the penalty area goes harmlessly over the target.
30:00 The ball is swung over by Jimmy Phillips, Kevin McIntyre makes a clearance.
27:19 A cross is delivered by Paul Boertien, blocked by Dave Hibbert.
26:32 Jake Robinson crosses the ball.
26:07 The ball is swung over by Paul Boertien, Graham Coughlan manages to make a clearance.
23:57 Joss Labadie fouled by Russell Penn, the ref awards a free kick. Free kick taken by Joss Labadie.
23:11 Foul by Robin Shroot on Graham Coughlan, free kick awarded. Kevin McIntyre restarts play with the free kick.
22:52 Jake Robinson takes a shot. Blocked by John McGrath.
22:10 Guy Branston produces a header from the edge of the box and misses to the left of the goal.
21:38 Craig Disley gives away a free kick for an unfair challenge on Jacques Maghoma. Free kick taken by Ryan Austin.
20:46 Richard Walker sends in a cross, clearance by Graham Coughlan.
19:26 The ball is swung over by Robin Shroot, Kevin McIntyre makes a clearance.
17:43 The ball is crossed by Russell Penn, Joss Labadie manages to make a clearance.
17:29 Paul Murray challenges Jimmy Phillips unfairly and gives away a free kick. Paul Boertien restarts play with the free kick.
16:53 The ball is sent over by Paul Boertien, Kevin McIntyre makes a clearance.
14:47 Richard Walker delivers the ball, save made by Chris Neal.
12:37 Kevin McIntyre concedes a free kick for a foul on Jacques Maghoma. Free kick taken by Ryan Austin.
10:44 Robin Shroot fouled by Dean Holden, the ref awards a free kick. Paul Boertien takes the indirect free kick.
9:27 Assist on the goal came from Dean Holden.
9:27 GOAL - Jake Robinson:Shrewsbury 1 - 0 Burton Albion Jake Robinson scores a goal from deep inside the penalty box to the bottom left corner of the goal. Shrewsbury 1-0 Burton Albion.
8:26 Free kick awarded for a foul by Robin Shroot on Dean Holden. Indirect free kick taken by Chris Neal.
6:09 Jimmy Phillips crosses the ball, clearance by Craig Disley.
5:23 Long range shot by Joss Labadie goes wide left of the target.
4:30 Free kick awarded for a foul by Jacques Maghoma on Joss Labadie. Paul Murray takes the free kick.
3:15 Dean Holden delivers the ball, Guy Branston manages to make a clearance.
1:52 Graham Coughlan gives away a free kick for an unfair challenge on Russell Penn. Marc Edworthy takes the free kick.
1:12 Jacques Maghoma fouled by Craig Disley, the ref awards a free kick. Jacques Maghoma restarts play with the free kick.
0:00 The referee gets the game started.
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Aldershot 3-1 Darlington
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