Bradley and Steele took control with an eagle by Steele on No. 14 and a birdie on No. 15, finishing at 32-under 184 for a three-stroke victory over two teams.
"We played well," Bradley said. "We got off to a slow start, kind of like we did all three days, but we played this last stretch of holes really well."
Steele added: "We had so much fun that it made it a lot easier for us."
Bradley and Steele had been talking about playing in Greg Norman's event since the spring, and said they weren't at the three-format event to "goof off."
Calcavecchia birdied No. 18 to give him and Price a 61, moving them into a tie for second at 187 with Rory Sabbatini and Jhonattan Vegas, who shot 60. Charles Howell III and Justin Leonard, and 2009 champions Jerry Kelly and Steve Stricker tied for fourth another shot back.
"We didn't hit a lot of good iron shots today," Price said. "We didn't put the ball close enough to the hole. We put a lot of pressure on our putting."
Bradley, the reigning PGA Championship winner, and Steele made seven straight birdies from Nos. 6 to 13, then Steele made an eagle putt from off the green, and followed that up with a 4-footer on No. 15 for birdie.
"That was a bonus," Steele said of the eagle.
On the next hole, Steele hit a 9-iron from 135 yards -- aiming at his wife, Anastasia, who was standing in the crowd behind the green -- to three feet.
"That was kind of where we couldn't really screw it up from there," Bradley said. "The shot was just spectacular."
Steele and Bradley birdied Nos. 8 and 9 to put a little distance between themselves and their playing partners, who parred both holes.
"They played really well together," said Price, who at 54 is a year older than Bradley (25) and Steele (28) combined. "They didn't make any mistakes."
Sabbatini and Vegas birdied five of the last seven holes to come out of a logjam and grab part of second.
"We played great," Sabbatini said. "We had some opportunities out there today and weren't able to capitalize on them. We had a fun time and that's what it's about."
Bradley and Steele had a chance at the tournament record of 34 under, but parred No. 16 and 18 coming in. Bradley, the nephew of former LPGA Tour and World Golf Hall of Famer Pat Bradley, and Steele shared $750,000 from the $3-million purse.