Brown (left) celebrates his goal with team-mate McDonald
Celtic maintained their three point lead at the top of the SPL after overcoming a determined Hibernian side.
Captain Stephen McManus fired the home side in front after 32 minutes shortly before Cillian Sheridan made it two.
Hibs pulled one back before half-time with Steven Fletcher's shot deflecting off Colin Nish into the net and Fletcher levelled just after the break.
Glenn Loovens headed Celtic back into the lead after 76 minutes and Scott Brown added Celtic's fourth late on.
Shaun Maloney stated Celtic's intention in the first minute when he combined with Scott McDonald before firing over the crossbar.
At the other end, Derek Riordan, who was making his first appearance against former club Celtic since re-joining Hibs, was given the chance to test Artur Boruc following a foul on Steven Fletcher.
From around 25 yards out, Riordan found the target but goalkeeper Boruc claimed comfortably.
Brown was presented with an opportunity after 19 minutes when Sol Bamba conceded possession midway inside the Hibs half.
The midfielder, who was playing against his former club, noticed goalkeeper Yves Ma-Kalambay off his line and attempted a chip, but the ball drifted over.
Hibs wasted a good opportunity to apply pressure to the Celtic defence on the counter attack when, in space on the right, Colin Nish's poor pass failed to reach any of his team-mates.
Riordan then drew an excellent one-handed save from Boruc with a deflected shot, the keeper having to adjust position to palm the ball out for a corner.
Andreas Hinkel (left) and John Rankin contest an aerial challenge
Steven Fletcher was almost in on goal after a neat through ball by Riordan but the Hibernian striker could not bring the ball under control as Celtic cleared the danger.
Within minutes, Celtic were in front asHibs failed to clear Shunsuke Nakamura's corner and McManus fired home from close range with his right foot.
McManus was then involved in Celtic's second, passing through to McDonald who flicked onto strike partner Sheridan.
The 19-year-old confidently took the ball beyond Yves Ma-Kalambay and passed into an empty net for his first goal for the club.
Undeterred by the deficit, Hibs continued to press forward and were rewarded on the 41st minute when Fletcher's shot from the right came off the head of Nish and flew into the net.
Dutchman Loovens was introduced after break with McManus failing to re-appear at the start of the second half.
Hibernian's equaliser came five minutes into the second half when Fletcher met Colin Nish's accurate back-post cross with a left-foot finish.
Celtic went back on the offensive but were foiled when Ma-Kalambay saved well from Andreas Hinkel and McDonald.
Maloney claimed for a foul after being challenged on the edge of the box by Lewis Stevenson, but the referee waved play on.
As the match entered the last quarter-of-an-hour, Barry Robson, who was deployed at left-back, saw his free-kick effort pushed around the post by Ma-Kalambay.
From the resultant corner, Maloney crossed for Loovens to head into the net, despite the presence of Lewis Stevenson on the line.
And Brown capped an excellent performance with a left-foot shot after Aiden McGeady's intelligent pass on 82 minutes.
Celtic manager Gordon Strachan: "It was a deserved victory for us. How we got back to 2-2, I never know.
"It was terrific game. Our attacking play was immense at times.
"Hibs had good spells but apart from that I thought we were phenomenal.
"Scott Brown was absolutely terrific, he did everything. He's got the lot, he just needs to tidy up his passing sometimes."
Hibernian manager Mixu Paatelainen: "I was pleased with the way we passed the ball and the way we created chances.
"Being 2-0 down at Parkhead is not an easy position to be in. To come back from that is a great achievement.
"Some of the goals we conceded were really sloppy goals to concede. I felt the two set-piece goals we conceded were absolute jokes. We must do better than that.
"There could have been more goals for us, unfortunately not."
Celtic: Boruc, Hinkel, Caldwell, McManus (Loovens 46), Robson, Nakamura (McGeady 63), Scott Brown, Hartley, Maloney, Sheridan, McDonald (McCourt 87). Subs Not Used: Mark Brown, Donati, O'Dea, McGowan.
Booked: McDonald, Hartley.
Goals: McManus 32, Sheridan 36, Loovens 76, Scott Brown 82.
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