Buddy Hield had 26 points to lead the Kings, who had six players score in double figures as they won their second straight after losing the previous three.
Westbrook had a season-high 34 points and James Harden added 27 points and 10 assists for Houston.
The game was tied earlier in the fourth when Westbrook dished it to Ben McLemore, whose 3-pointer made it 116-113 with 22.7 seconds to go. Hield missed a 3-pointer after that, but Bogdan Bogdanovic grabbed the rebound and got it back to Hield, who didn’t miss this time to tie it again with 8.4 seconds left.
Westbrook tied it earlier in the period on a layup before Harrison Barnes made it 113-110 with a 3-pointer. The lead was short-lived as Westbrook made a 3 seconds later to tie it again with about a minute left.
The Kings led by six after a 3-pointer by Yogi Ferrell with about 9 minutes left. The Rockets scored the next four points before Bogdanovic’s 3-pointer pushed Sacramento’s lead to 105-102 midway through the quarter.
Houston got four quick points from Clint Capela before Harden made two free throws to put the Rockets on top 106-105 with 4 1/2 to play.
Harden had a 3-pointer waved off late in the third quarter when he was called for an offensive foul. Coach Mike D’Antoni challenged the call, but it was upheld. Joseph had a three-point play on the other end before Harden made a 3-pointer. This time Trevor Ariza was called for a foul on Harden and Sacramento coach Luke Walton challenged the call. Officials ruled that Ariza did foul Harden, but that it was before the shot so three points were taken off the board.
Harden made both free throws to put Houston on top, but Barnes added a pair of free throws for Sacramento after that to leave the Kings up 94-93 entering the fourth quarter.
Kings: F Marvin Bagley (broken right thumb) is getting close to a return after missing 22 games with his injury, but Walton wouldn’t say exactly when he expects him to return. … Bjelica had 17 points and made three 3-pointers. … Barnes had 19 points and eight rebounds.
Rockets: C Tyson Chandler missed a second straight game with flu-like symptoms. … G Austin Rivers sat out with an illness. … P.J. Tucker had 10 points for his fifth game with at least 10 points in the last seven. … Houston outrebounded Sacramento 51-37.
Kings: Host Oklahoma City on Wednesday night.
Rockets: Visit Cleveland on Wednesday night.