Crane made a 12-foot birdie on the fourth extra hole to beat Van Pelt. Caron was eliminated with a bogey on the second playoff hole.
All three players tied at 23-under 261 after 72 holes at the Whirlwind Golf Club in suburban Phoenix.
'It's been an incredible year and incredible week,' said Crane, choking back his emotions. 'I just prayed at the beginning of the week and followed my theme. The whole thing is pretty awesome.'
Crane began the final round at 20-under par and with a one-stroke lead over Van Pelt, with whom he had shared the first- and second-day leads. Caron was four off the pace.
At one point, four players shared the lead at 21-under. However, Van Pelt put himself in position to win when he stuffed in a birdie at the par-5 17th to go 24-under and one up on Crane and Caron, who had already finished.
But, Van Pelt let the two back in when he three-putted the final hole from 40 feet, missing a 3-footer that would have given him his first career win.
Van Pelt's slip allowed Crane and Caron to join a playoff for the $76,500 payoff.
The threesome went back to the 18th tee for the first extra hole, where all three two-putted for pars. Caron was eliminated on the second trip up 18 when he yanked a 9-iron left of the green and failed to get up and down. Van Pelt had the upper hand again, but missed a 20-footer for birdie.
On the third extra hole, again the 442-yard 18th, Crane watched his 6-foot birdie slide over the right edge and the pair went back to the 18th tee box for a fourth and final time.
Van Pelt's 3-wood wound up in the right rough while Crane was off the fairway to the left. Van Pelt's 9-iron approach failed to hold the green and wound up just over the back, some 60 feet from the pin. Crane left his about 12 feet past the cup.
When Van Pelt's chip stopped 4 feet short, it left the door open a second time for Crane to end matters.
'It was neck-and-neck all day,' said Crane, who hit 16 greens during the final round. 'I was just trying to stay focused during the playoff. I was just trying to hang in there and not put a time limit on things.'
Crane, winner of the 2000 Buy.Com Wichita Open as a Monday qualifier, finally ended things by rolling in the putt that vaulted him to No. 26 on the money list with just two events left on the schedule. The top 15 players at the end of the year will earn their 2002 PGA TOUR cards.
Full-field scores from the Buy.Com Gila River Classic