DeChambeau birdied the par-five 18th for a 5-under 66 while Lee birdied four of his last six holes for the same score as both players finished on 14-under 274 at Sentosa Golf Club.
Veteran Englishman Lee Westwood closed with a 70 to finish third, his best finish in LIV.
Australia's Cameron Smith matched DeChambeau and Lee's final-round 66 to secure a share of eighth place with American Matthew Wolff for a 276 tally, while compatriot Marc Leishman finished two shots back on joint 15th after a final score of 70.
Lee was trying to become the first wildcard — players not affiliated with a team — to win in the LIV Golf League.
It looked certain the playoff would go another hole when Lee had a 2-footer for par but he jabbed at it with a quick stroke and it spun out hard off the left lip.
"It was a short putt and I wanted to just hit it hard, and I hit it a little too hard," Lee said.
"I think the adrenaline was pumping a little bit."
DeChambeau put his hands over his head in disbelief when Lee missed the playoff putt.
He said it reminded him of John Daly having a 15-foot birdie putt to beat Tiger Woods in a World Golf Championships playoff in 2005, only to three-putt by missing a 3-foot par putt.
"To actually see that happen in front of you, for you to be the positive receiving side of it, it's just a weird feeling," DeChambeau said.
"But it's a win and something I'll appreciate for the rest of my life. Even if I lost today, I was still looking pretty good at my game. I was excited the way I was striking it coming in the last couple days."
It was DeChambeau's first victory over 72 holes since he won the US Open at Pinehurst in 2024, and it was his fourth title on LIV Golf.
Jon Rahm finished fifth, ending a stretch of five tournaments he won or was runner-up.
The 4 Aces captained by Dustin Johnson won the team competition for the second straight week.
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