A turnover by James Harden gave the Thunder the ball back and Derek Fisher made two free throws to push the lead to 3. Harden made a layup, but Reggie Jackson hit two more free throws after that.
Houston had a last chance, but Carlos Delfino's 3-pointer fell short.
Harden scored 30 points to lead the Rockets in the first playoff game in Houston since 2009.
Game 4 is Monday night in Houston
Westbrook was injured in Game 2 and had season-ending knee surgery Saturday. It was the first time Durant had ever played without Westbrook, who hadn't missed a game in his career before Saturday.
Durant tied a career high for the playoffs, and he added 14 rebounds, four assists, two steals and a block. Jackson started in place of Westbrook and had 14 points, and Ibaka added 17 points and 11 rebounds.
A 3-pointer by Chandler Parsons tied it with 5:46 left and Delfino gave Houston its first lead since early in the first quarter, 94-93, about 2 minutes later.
Ibaka made four straight points after that, ending with a reverse layup, to make it 97-94 with about a minute and a half left.
Harden hit a pair of free throws. Then Francisco Garcia's 3-pointer put them up 99-97 with 45 seconds left, before the clutch shot by Durant.
The Rockets rallied from a 15-point deficit to take a lead in the fourth quarter in Game 2. But they weren't able to hold on and Oklahoma City got the 105-102 win.
Westbrook's absence didn't seem to bother Oklahoma City early, as Durant had the big first half and the Thunder looked to be in complete control.
P Monday, 7:30 p.m.
TV • TNT
Oklahoma City leads 3-0