He did so by again mirroring his father, NBA Hall of Famer Rick Barry.
Canyon made all four of his underhanded free throws in the Gators' 71-62 win over Texas A&M to break the mark. He has made 39 in a row, topping the former mark (37) set by Taurean Green during the 2005-06 season.
Rick Barry famously shot his free throws underhanded throughout his career.
Canyon Barry hasn't missed a free throw in nine games and is shooting close to 90 percent for the season.
"Trying to keep it rolling, trying to get to 90 percent,'' Barry said after Saturday's game. "I think I'm close now hopefully, but just step to the line, have confidence every time. It doesn't really mean much. I just care about winning, getting these guys ready for the next game.''