Also the winner in 2019, Conners shot a closing four-under 68 at TPC San Antonio' on Sunday for a 15-under total as he secured his second PGA Tour victory.
He now heads to the Masters, where he tied sixth last year for his second straight top-10 finish at Augusta National.
"I had been feeling really good about my game, and looking forward to getting back here to San Antonio," Conners said.
"When I won in 2019, it was different, a real roller-coaster final round. I dug deep on the back nine, so I tried to channel that part of it today."
A shot behind Patrick Rodgers starting play, Conners had a three-shot lead after he birdied No.15. Stevens eagled the 17th, but missed a nine-foot birdie putt at 18 that would have tied it. Connors ended it with a three-foot par putt on 18.
Stevens shot a 66. Sam Ryder (66) and Matt Kuchar (68) followed at 13 under.
Rodgers saw a chance for his first tour victory and first Masters spot slip away. He shot a 73 to finish fifth at 11 under.
Conner's best finish since hoisting the 2019 Texas Open trophy was a third-place effort at the Arnold Palmer Invitational last year.
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