Parsons added 23 points for Houston and Terrence Jones had 16 points and 11 rebounds.
Oklahoma City was up by one before Houston scored seven straight points to take a 104-98 lead with less than three minutes left. The Rockets made four free throws before a 3-pointer by Garcia.
The Rockets started the fourth quarter with 3-pointers by Jeremy Lin, Isaiah Canaan and Harden for a 9-2 spurt which gave them a 91-86 lead with about 10 minutes left. Durant scored the next four points to get Oklahoma City within 91-90.
Houston scored the last six points of the third quarter to cut the lead to 84-82 entering the fourth quarter.
The Thunder scored 39 points in the third quarter to take the lead after trailing the entire game. They opened the second half with a 9-0 run punctuated by a dunk by Ibaka to make it 54-52. Houston went right back on top with a 3-pointer by Parsons, but a 9-2 spurt by the Thunder gave them a 63-57 lead with about seven minutes left in the quarter.
The Thunder trailed through the first quarter and cut it to three points early in the second quarter on a 3-pointer by Caron Butler before an 11-0 run by Houston pushed the lead to 43-29 about five minutes before halftime. Harden scored the last seven points in that span and capped it by making a 3-pointer with Derek Fisher right in his face.
Durant scored Oklahoma City's final five points to get the Thunder within 50-45 at halftime. The first three points of that run came when Durant was fouled on an off-balance layup he made with his back to the basket and then made the free throw.
NOTES: The 39 points the Thunder scored in the third quarter were the most anyone has scored against Houston this season in the quarter. ... Hall of Famer Hakeem Olajuwon watched the game from a courtside seat. ... The win was Houston's 50th, giving them the 10th 50-win season in franchise history.