The trio finished regulation at 11-under-par 277 before an electrical storm rolled through Portmarnock Golf Club, stopping play for over a half hour. When the weather cleared and the playoff began, Campbell took full advantage.
Campbell was the first to play the par-4 18th and split the fairway with his drive. Bjorn followed and found the rough off the tee while Hedblom left his drive in the first cut.
The New Zealander hit a remarkable second shot and nearly holed out for an eagle. His ball stopped within a foot of the hole, putting all of the pressure on Bjorn and Hedblom.
Bjorn hit his approach to the left side of the green and had 18 feet for birdie. Hedblom's second stopped 20 feet short of the putt, the same distance he had for a par-saving putt on the 18th in regulation.
Hedblom and Bjorn could not convert and Campbell walked up to his ball and sent it to the bottom of the cup for his sixth career victory on the European Tour.
The victory kickstarts Campbell's commitment to pass on the PGA Tour in order to play full time on the European Tour.
'A combination of a lot of things have made me more settled,' said Campbell. 'I am more comfortable here than that side of the Atlantic and I am here looking forward to playing some golf over the next month or so. I will play two events in the States then come back here to play the rest of the European Tour.'
Campbell found himself out of contention throughout the 2003 season until this week. He shot 66 on Thursday, his best opening-round score of the year, and worked his way into a three-way tie for the lead after 54 holes at 10-under par.
He suffered a bogey at the second to drop to minus-9 but bounced back with a birdie at the sixth. Campbell ran home a putt from the fringe for a birdie at the ninth and hit his second shot to 10 feet for a birdie at the 10th to reach 12-under as the first drops of rain began to fall.
Campbell found the sand with his second shot at the 11th but his bunker shot hit the wall of the trap and bounced back. He scrambled for a bogey en route to a round of 71.
Bjorn, who was seeking to shake the demons of his late collapse at last week's British Open championship, came up short on the greens on Sunday. He started with a bogey at the first but countered with a two-putt birdie at the sixth and squandered several chances the rest of the way.
The Dane missed a birdie chance at the par-5 13th but managed to convert on a six-foot putt at the 16th to join the leaders at 11-under. Bjorn had another birdie opportunity at the 17th but missed a 12-foot putt left.
'It's nice to be among the contenders again,' said Bjorn, who carded a 71 on Sunday. 'I've struggled the last three or four months. All I can do is control my own emotions and the golf ball, hit it, find it and see what happens.'
Hedblom had the low round of the day with a 68 to work himself into the playoff.
The Swede was three shots off the lead to start the day but found himself moving up the leaderboard with a birdie at the third. Hedblom added a birdie at the ninth to make the turn at 9-under but stumbled with a bogey at the 11th.
At the par-4 14th, Hedblom sent his second shot to 15 feet and drained the putt for the first of three consecutive birdies to move to minus-11. Hedblom closed his round with a crucial par save at the last to earn a spot in the extra session.
England's David Lynn, who shared the 54-hole lead with Bjorn and Campbell, carded a 1-over 73 to join fellow countryman Greg Owen in a tie for fourth at 9-under-par 279. Germany's Sven Struver was one shot further back at 8-under-par 280.
Robert Karlsson of Sweden finished five shots off the lead at 6-under-par 282 along with Australia's Peter Lonard.
Gary Murphy was the leading Irishman in the field in a group at 4-under-par 284.