In Game 5, he made nine of his first 11 shots from the field and wound up playing 41:34 despite his illness.
The streaky Rockets were due for a good shooting night from beyond the 3-point arc and it arrived Wednesday by shooting 40 percent (14 for 35).
Six Houston players scored in double-digits compared to three for the Thunder.
Rockets center Omer Asik had 21 points, 11 rebounds and converted 13 of 18 free throws (72.2 percent) after being intentionally fouled seven times in the fourth quarter.
The Thunder tried a Hack-An-Asik tactic in an effort to narrow the deficit with some missed free throws from Asik, who entered the game having shot 58.8 percent from the line in the series.
Making only his second start, Francisco Garcia went 5 for 12 on 3-pointers and added 18 points. Point guard Patrick Beverley, despite being booed due to his role in Russell Westbrook's season-ending knee injury, had 14 points and eight rebounds, while Chandler Parsons and Aaron Brooks added 10 points each.
The Rockets shot 47.2 percent from the field compared to 41.9 percent for OKC.
“They came out and played lights out,” Thunder coach Scott Brooks said. “They shot the ball so well.”