Harden scored 38 points and grabbed 10 rebounds as the Rockets dug out of an 0-2 hole with another scrappy defensive performance Monday night.
"When you're dealing with these guys, if you let Klay [Thompson] and Steph [Curry] run around and shoot 3s, you don't have no chance," Harden told reporters. "The only chance we have is to be in to their bodies and make every shot that they take contested."
The Rockets led by as much as 15 points early in the fourth quarter. Houston's lead dwindled to nine before the Warriors rattled off the next seven points. Golden State point guard Stephen Curry drained a 3-pointer with 19 seconds left to cut the Warriors' deficit to 110-108.
Harden converted one of two free throws with 11.5 seconds remaining. The Warriors had prime scoring chances to tie the game, but Kevin Durant and Curry each missed 3-pointers. Rockets point guard Chris Paul was intentionally fouled and iced the game by making one of two free throws with 2.9 seconds left.
"We got a couple of wide-open looks," Durant told reporters. "They just didn't fall for us."
Durant had 34 points, seven rebounds and five assists in 43 minutes. Curry, who shot 7-for-23 in Game 3, scored 11 points in the first quarter. He had 30 points (12-of-25 shooting), eight assists and four boards.
Houston guard Eric Gordon had 20 points and four rebounds. Paul registered 13 points, eight rebounds and five assists. Rockets forward PJ Tucker had a double-double with 17 points and 10 rebounds.
Game 5 is Wednesday night at Oracle Arena in Oakland, Calif.