Bournemouth put the absence of Brett Pitman aside to earn a comfortable first away win of the season.
The striker looks set to join Bristol City after rejecting Blackpool but his team-mates continued their recent scoring spree at Tranmere.
Josh McQuoid fired past Joe Collister before Michael Symes netted from the spot after Ian Goodison tripped him.
And Marc Pugh's angled drive in off the post on the break made it eight goals in two games for the on-song Cherries.
Tranmere manager Les Parry told BBC Radio Merseyside: "When we advanced up the pitch, our quality started to suffer. When we gave them the ball they were good at counter-attacking us very quickly.
"That's what caused us all the problems. At home against a team like that we are going to struggle if we don't keep the ball.
"Performance-wise, it wasn't as bad as the result would suggest but Bournemouth will be there or thereabouts as they're not a bad side."
Bournemouth manager Eddie Howe told BBC Radio Solent: "It was a good performance, I thought we were a real threat.
"We had a specific game plan, and the lads executed it perfectly
"We're disappointed to lose Brett - anyone who's been watching us the last year and a half will see what a good player he is."
90:00+1:54 Nick Wood gives away a free kick for an unfair challenge on Jayden Stockley. Direct free kick taken by Shwan Jalal.
90:00+1:36 The referee blows for offside against Jayden Stockley. Free kick taken by Aaron Cresswell.
90:00+0:59 Aaron Cresswell produces a right-footed shot from just outside the penalty box that misses to the left of the goal.
90:00+0:06 Inswinging corner taken by John Welsh, Danny Hollands manages to make a clearance.
90:00 The referee brings the game to a close.
87:15 Shot from just outside the penalty box by Enoch Showunmi misses to the left of the target.
86:34 Marc Pugh takes a shot. Save made by Joe Collister.
86:15 A cross is delivered by Aaron Cresswell, Jason Pearce manages to make a clearance.
85:35 John Welsh takes the inswinging corner, save by Shwan Jalal.
84:57 Unfair challenge on Liam Darville by Marc Pugh results in a free kick. Joe Collister takes the direct free kick.
84:22 Effort from deep inside the area by Aaron Cresswell clears the bar.
83:59 Lee Bradbury takes a shot. Save by Joe Collister.
82:14 Substitution Jayden Stockley replaces Michael Symes.
82:14 Corner taken by Marc Pugh from the left by-line played to the near post, clearance by Kithson Bain.
Correction - 82:14 Substitution Michael Symes leaves the field to be replaced by Jayden Stockley.
Correction - 82:14 Corner taken by Marc Pugh from the left by-line to the near post, clearance by Ryan Fraughan.
81:33 Anton Robinson fouled by Kithson Bain, the ref awards a free kick. Shaun Cooper takes the direct free kick.
Correction - 81:33 Ryan Fraughan concedes a free kick for a foul on Anton Robinson. Free kick taken by Shaun Cooper.
80:06 The referee gives a free kick against Marc Pugh for handball. Direct free kick taken by Joe Collister.
79:17 Marc Pugh is flagged offside by the assistant referee. Joe Collister takes the direct free kick.
78:31 A cross is delivered by Liam Darville, clearance made by Shaun Cooper.
76:57 Marvin Bartley fouled by Enoch Showunmi, the ref awards a free kick. Shwan Jalal takes the direct free kick.
75:45 Substitution (Bournemouth) makes a substitution, with Danny Hollands coming on for Liam Feeney.
74:34 The assistant referee flags for offside against Liam Feeney. Free kick taken by Joe Collister.
72:23 Nick Wood takes a inswinging corner.
71:24 Enoch Showunmi produces a left-footed shot from just outside the penalty box that misses to the left of the goal.
68:47 Kithson Bain gives away a free kick for an unfair challenge on Liam Feeney. Anton Robinson takes the direct free kick.
Correction - 68:47 Ryan Fraughan gives away a free kick for an unfair challenge on Liam Feeney. Direct free kick taken by Anton Robinson.
67:36 Substitution Ian Thomas-Moore goes off and Adam McGurk comes on.
66:43 Terry Gornell produces a left-footed shot from long range that goes harmlessly over the bar.
66:27 The ball is delivered by Kayleden Brown, clearance made by Shaun Cooper.
65:39 The ball is delivered by Liam Darville, Ian Thomas-Moore takes a shot. Save by Shwan Jalal.
Correction - 62:28 Substitution Joss Labadie goes off and Ryan Fraughan comes on.
Correction - 62:28 Substitution Lee Bradbury replaces Josh McQuoid.
62:28 Substitution Kithson Bain comes on in place of Joss Labadie.
62:28 Substitution Josh McQuoid leaves the field to be replaced by Lee Bradbury.
61:17 Booking Booking for Ian Thomas-Moore for unsporting behaviour.
60:31 Josh McQuoid provided the assist for the goal.
60:31 GOAL - Marc Pugh:Tranmere 0 - 3 Bournemouth Marc Pugh finds the net with a goal from inside the six-yard box to the bottom right corner of the goal. Tranmere 0-3 Bournemouth.
Correction - 59:44 Joss Labadie gives away a free kick for an unfair challenge on Anton Robinson. Free kick taken by Jason Pearce.
59:44 Foul by Joss Labadie on Anton Robinson, free kick awarded. Liam Feeney restarts play with the free kick.
Correction - 58:08 Marc Pugh takes a shot. Save by Joe Collister.
58:08 Marc Pugh takes a shot. Save made by Shwan Jalal.
57:33 Free kick awarded for an unfair challenge on Marvin Bartley by Joss Labadie. Shwan Jalal takes the free kick.
57:07 Shaun Cooper gives away a free kick for an unfair challenge on Ian Thomas-Moore. Direct free kick taken by John Welsh.
56:09 Unfair challenge on Anton Robinson by Terry Gornell results in a free kick. Direct free kick taken by Rhoys Wiggins.
55:37 Long range effort from Ian Thomas-Moore misses to the left of the goal.
54:02 The assistant referee flags for offside against Michael Symes. Free kick taken by Liam Darville.
49:49 Liam Darville challenges Marvin Bartley unfairly and gives away a free kick. Indirect free kick taken by Jason Pearce.
48:13 Foul by Michael Symes on Nick Wood, free kick awarded. Joe Collister takes the free kick.
47:15 Free kick taken by John Welsh.
47:15 Booking Anton Robinson booked for unsporting behaviour.
47:01 Anton Robinson gives away a free kick for an unfair challenge on Enoch Showunmi.
45:15 Kayleden Brown fouled by Marvin Bartley, the ref awards a free kick. John Welsh takes the free kick.
45:01 Substitution Paul McLaren goes off and Kayleden Brown comes on.
45:01 The referee blows his whistle to start the second half.
Half Time
45:00+1:12 Free kick awarded for a foul by Joss Labadie on Rhoys Wiggins. Shwan Jalal takes the indirect free kick.
45:00+0:05 Joss Labadie takes a shot. Shwan Jalal makes a save.
45:00 The referee blows for half time.
43:58 Indirect free kick taken by Rhoys Wiggins.
43:58 Booking Joss Labadie receives a yellow card for unsporting behaviour.
43:49 Joss Labadie challenges Marvin Bartley unfairly and gives away a free kick.
43:09 Free kick awarded for an unfair challenge on Joss Labadie by Anton Robinson. Free kick crossed right-footed by Paul McLaren, save by Shwan Jalal.
42:18 Marvin Bartley has an effort at goal from outside the penalty box which goes wide right of the target.
41:10 Header by Enoch Showunmi from deep inside the penalty area misses to the left of the target.
37:45 Strike comes in from Aaron Cresswell from the free kick.
37:45 Booking The referee shows Stephen Purches a yellow card for unsporting behaviour.
37:27 Free kick awarded for an unfair challenge on John Welsh by Stephen Purches.
35:35 Rhoys Wiggins takes a inswinging corner from the left by-line to the near post, clearance by Paul McLaren.
35:13 Rhoys Wiggins sends in a cross, Joe Collister makes a save.
34:26 Michael Symes takes a shot. Joss Labadie gets a block in.
32:56 Corner taken by Marc Pugh.
32:41 Josh McQuoid takes a shot. Blocked by Ian Goodison.
31:15 Aaron Cresswell gives away a free kick for an unfair challenge on Michael Symes. Free kick taken by Shaun Cooper.
29:47 Corner taken right-footed by Paul McLaren from the right by-line, save by Shwan Jalal.
29:35 Aaron Cresswell sends in a cross, clearance made by Rhoys Wiggins.
27:43 Centre by Terry Gornell, clearance by Rhoys Wiggins.
Correction - 25:47 The official flags Enoch Showunmi offside. Free kick taken by Shwan Jalal.
25:47 The offside flag is raised against Enoch Showunmi. Shaun Cooper takes the free kick.
24:57 Free kick awarded for an unfair challenge on Marvin Bartley by John Welsh. Shaun Cooper takes the indirect free kick.
23:54 Indirect free kick taken by Paul McLaren.
23:54 Booking Josh McQuoid goes into the referee's book for unsporting behaviour.
23:38 Josh McQuoid gives away a free kick for an unfair challenge on Liam Darville.
22:51 Anton Robinson gives away a free kick for an unfair challenge on Enoch Showunmi. Free kick taken by Liam Darville.
21:57 Anton Robinson challenges John Welsh unfairly and gives away a free kick. Indirect free kick taken by Joe Collister.
20:55 Foul by Enoch Showunmi on Rhoys Wiggins, free kick awarded. Shaun Cooper takes the indirect free kick.
19:28 Corner taken by Paul McLaren from the right by-line, clearance by Shaun Cooper.
18:44 Anton Robinson has a shot on goal from outside the area which misses right.
17:25 GOAL - Michael Symes:Tranmere 0 - 2 Bournemouth Placed penalty scored by Michael Symes. Tranmere 0-2 Bournemouth.
16:53 Booking Ian Goodison shown a yellow card.
16:20 Michael Symes fouled by Ian Goodison, the ref awards a Penalty.
14:29 Liam Feeney sends in a cross, clearance by Liam Darville.
14:10 Enoch Showunmi produces a cross, save made by Shwan Jalal.
10:55 The referee blows for offside against Michael Symes. Joe Collister takes the direct free kick.
10:26 The ball is sent over by Marc Pugh, save by Joe Collister.
7:46 The assist for the goal came from Michael Symes.
7:46 GOAL - Josh McQuoid:Tranmere 0 - 1 Bournemouth Josh McQuoid gets on the score sheet with a goal from inside the area low into the middle of the goal. Tranmere 0-1 Bournemouth.
7:00 Marvin Bartley concedes a free kick for a foul on Joss Labadie. Paul McLaren restarts play with the free kick.
5:36 The ball is sent over by Terry Gornell, Jason Pearce manages to make a clearance.
5:02 Liam Darville crosses the ball, save by Shwan Jalal.
3:03 Terry Gornell sends in a cross, save made by Shwan Jalal.
1:56 The ball is delivered by Marc Pugh, Aaron Cresswell manages to make a clearance.
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