Jackson finished with 18 points in his second start in place of Westbrook, and Kevin Martin added 16.
Houston got 17 points from Omer Asik and 13 from Carlos Delfino.
Oklahoma City’s DeAndre Liggins received a technical foul with :07 left in the third quarter for arguing the call on a jump ball.
Delfino made the free throw, but Durant hit a jump shot at the buzzer to get the Thunder within 91-84 entering the fourth quarter.
The Rockets led by two points in the third quarter before a 3-point play by Harden. He took Jackson off the dribble for a jump shot and drew the foul — Jackson’s fourth — to send him to the bench and the crowd into a frenzy.
Durant was shaken up a few seconds later when he crashed into the scorer’s table chasing a loose ball. He remained on his back for a couple of minutes holding his right wrist before being helped to his feet. But he didn’t leave the game and seemed to be OK.
Harden’s three-point play was the start of a 12-2 Houston run capped by another three-point play — this one by Delfino — to extend the lead to 85-75 with about three minutes left in the third quarter.
Delfino dunked after stealing the ball from Martin, and Durant fouled him on the play.
Houston scored the first 10 points of the second half to erase a halftime deficit and take a 63-60 lead. Parsons had six points in that span.
The Rockets did a much better job of keeping the crowd involved in this one than they did in Game 3, when they trailed early by as many as 26 points. Houston rallied to take a lead in the fourth quarter of that game before losing 104-101.
Near the end of the first half Durant sailed into the crowd Superman-style to save the ball on a bad pass from Harden. He was able to get to his feet and stood in the crowd watching as Martin swished a 3 on the other end. He couldn’t figure out how to get out of the crowd for a few seconds before finally climbing out and back onto the court. But before he got back to the game Durant asked a woman in the first row who he crashed into if she was OK.