Surviving an errant drive that ended up in the water and led to a bogey on the par-five 16th at the Memorial Park layout, Perth product Lee then showed nerves of steel on the 18th with an up and down from off the green to save par and shoot a final-round 67 to finish at 20-under.
It was just enough to get the better of Scheffler and Gary Woodland, who both finished at 19-under after shooting respective final rounds of 63 and 62.
The win was Lee’s first in 56 PGA Tour events and his first victory anywhere since his Australian PGA Championship triumph at Royal Queensland in November 2023.
It was also a timely return to winning form for Lee ahead of the first major of the year, the Masters, which starts at Augusta on Thursday week.
“It’s unbelievable,” said Lee, who led by four strokes after the third round.
“It was a big mental grind and I’m very proud. Scottie was right there, and it was nerve-racking.
“I’ve been playing a lot of good golf over the last couple of months, so to get it done … I’m so proud.
“Let’s keep it going.”
At this year’s Players Championship, Lee was the co-leader after 36 holes but fell away over the final two rounds to finish in a tie for 20th.
Lee tied for sixth at the Players Championship in 2023 after shooting 76 in the final round before sharing fifth place at that year’s US Open.
Last year he finished runner-up at the Cognizant Classic and the Rocket Classic.
Lee’s win in Houston has moved him from 55th to a career-high 22nd in the official world golf rankings, making him the highest-ranked Australian player ahead of Adam Scott (32) and Jason Day (36).
The Victory also lifted Lee to 16th in the FedExCup standings.
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