Australia's Stuart Appleby, the overnight leader, struggled throughout his round on his way to a four-over 76. He finished alone in second place at 12- under-par 276.
Adam Scott and Scott Verplank were one stroke further back at minus-11.
Tiger Woods, who was trying to win this event for a record fifth straight time, managed a one-over 73 and completed the event at even-par 288.
The only history made on Sunday was Campbell's comeback. He turned a four- stroke deficit into a six-shot win over the final 10 holes at Bay Hill Golf Club and Lodge.
'I knew I had a long road to go today, so I just stayed real patient,' said Campbell, who picked up $900,000 for his second PGA Tour win. 'I really started to make a move on the back nine and he (Appleby) made a couple of bogies and with that I moved into the lead.'
Campbell got his round going with a birdie at the par-three second, but Appleby again climbed four strokes clear of Campbell when he birdied the sixth from six feet out.
Campbell's comeback really got going with back-to-back birdies from the eighth to move to 15-under-par. Appleby, meanwhile, bogeyed the ninth to drop to minus-16.
'Nine definitely was a turning point,' Appleby said. 'I didn't hit a great drive and thought I hit a really good second shot. Left myself in a vulnerable position and he holes the putt, and I was like, okay, he's holed his. Then I didn't make mine.'
The par-four 11th proved to be another turning point. Appleby found a fairway bunker off the tee and knocked his second into greenside bunker. Appleby was unable to save his par from there and fell into a tie for the lead at 15- under.
Both players birdied the par-five 12th to get to 16-under.
The Australian fell out of the lead for good with a three-putt bogey at the 14th. Campbell then created some breathing room for himself.
He rolled home a birdie putt at the 15th from 25 feet out. Campbell then two- putted for birdie at the par-five 16th to grab a three-shot lead.
Appleby continued his slide from the top. He three-putted from the back of the green on 17 for bogey and took two penalty strokes en route to a double-bogey at the last.
Campbell, who played with tournament host Arnold Palmer during the opening two rounds, calmly two-putted for par on each of the last two holes to earn his first title after last year's Tour Championship.
'Playing with him the first two days was so awesome,' said Campbell of his pairing with Palmer. 'It was such a good experience for me. Especially not knowing how many more tournaments he'll play in and just getting the experience of playing with him was such an inspiration.'
Appleby lost for the first time when holding the lead entering the final round. Three times previously he had held at least a share of first entering the final round and all three times he went on to win.
'I really screwed up the back nine,' said Appleby. 'I felt all right all day, but Chad just kept making every putt. I was trying to just ignore that and continue to do what I needed to do and hit my shots. It just was a day where I think he played great.
'Playing with Chad for two days, looking back now, I can't even think of a poor shot he hit in two days. He hardly dropped a shot in two days. Great golf, great golf.'
Jerry Kelly used a three-under 69 Sunday to climb into fifth place at 10- under-par 278. First and second round leader Shigeki Maruyama stumbled to a closing one-over 73 and shared sixth place at eight-under-par 280 with Stephen Ames, Darren Clarke and Zach Johnson.
John Daly, who won the Buick Invitational earlier this year, closed with an entertaining round of 73. He had three birdies over four holes on the front nine.
Then to close his round, Daly posted double-bogey on 15, eagle on 16, bogey on No. 17 and double-bogey at the last. He finished at minus-seven, where he was joined by Dennis Paulson.