Oklahoma City survived a fourth-quarter comeback to take a 2-0 lead in the Western Conference quarterfinal series, which will resume Saturday in Houston.
Despite losing point guard Jeremy Lin during the first half with a muscle contusion in his chest, Houston put on a 16-0 run in the final period to take a 95-91 lead.
The Thunder then went on a 10-2 surge to regain the lead, the key basket coming when Durant launched a 3-pointer that put Oklahoma City in front 98-97. Thabo Sefolosha then hit a 3-pointer to extend the Thunder's lead to four points with 1:01 to play and they held on at the free throw line.
Kevin Martin wrapped up the victory by hitting 1-of-2 from the line with 12 seconds remaining to put the Thunder ahead by four.
Both Durant and Russell Westbrook scored 29 points, but combined to make just 20-of-51 from the field.
Serge Ibaka added 12 points and 11 rebounds for the Thunder, who shot 43 percent from the field, made 11-of-34 from 3-point range and suffered a 57-40 rebounding deficit.
James Harden led Houston with 36 points and 11 rebounds. He connected on only 9-of-24 from the field, but was 17-of-20 from the foul line. Chandler Parsons was held to 7-of-23 in his field goal attempts.
Oklahoma City appeared to have put the game away with an 11-0 run in the third period that gave the Thunder a 74-63 advantage, but Houston battled back with its outburst that began with 8 minutes to play.
Oklahoma City went scoreless for almost 5 minutes while the Rockets were getting back in the game.