LOS ANGELES -- A stunning reversal in fortune allowed the Houston Rockets to force a Game 7.

Guard James Harden scored 23 points, and center Dwight Howard added 20 points and 21 rebounds, rallying the Rockets to a 119-107 victory over the Los Angeles Clippers on Thursday night and tying the Western Conference semifinal series at three games apiece.

Game 7 is Sunday at the Toyota Center in Houston. The winner advances to the Western Conference finals against either the Golden State Warriors or the Memphis Grizzlies.

"We have to be able to soak this up, see what we did right the last quarter-and-a half and mimic that," said Rockets forward Josh Smith, who scored 14 of his 19 points and made three of his four 3-pointers in the fourth quarter. "All year long, we fought through a lot of adversity. It's just a testament to what we did throughout the season."

The Clippers led 100-88 with less than eight minutes remaining before a 24-2 run saved Houston's season.

"We didn't finish. When we got that lead, we got comfortable," said Clippers point guard Chris Paul, who compiled 31 points, 11 assists and seven rebounds. "Coming out of one of those timeouts, I told our guys to play more freely and with confidence. Unfortunately, things didn't work out our way."

Rockets reserve forward Corey Brewer contributed 19 points, 15 of them in the final period, including a 3-pointer that gave Houston the lead for good with 3:42 left. He also grabbed 10 rebounds. Forward Terrence Jones finished with 16 points for the Rockets, who had six players score in double figures.

Forward Blake Griffin had 28 points and eight rebounds for the Clippers, who led 3-1 in the series before dropping the past two contests.

Los Angeles wilted down the stretch Thursday. A three-point play by backup point guard Austin Rivers gave the Clippers a 12-point advantage with 7:38 remaining in the game, but the Rockets surged to a 112-102 lead after a free throw by Smith with 1:16 left.

"Guys did an amazing job," said Harden, who didn't play in the fourth quarter despite not being injured, saying it was a mutual decision between him and coach Kevin McHale. "It was unbelievable."

The Rockets outscored the Clippers 40-15 in the fourth while outshooting Los Angeles 63.2 percent (12 of 19) to 18.2 percent (4 of 22). Houston made seven of 11 3-pointers to only two of nine for the Clippers in the fourth.

A 26-5 overall margin in second-chance points also benefitted Houston.

"It's not an ideal situation to play in where you're missing shots," said Griffin, who was scoreless and missed all five of his attempts in the final quarter. "Seemed like they were hitting everything."

As they had in Games 3 and 4, both losses, the Rockets endured a rough time in the third quarter, but this time they survived it. The Clippers bolted from a 64-62 halftime lead with a 13-4 surge to open the third for a 77-66 cushion after a three-point play by Paul.

Things got a bit testy less than two minutes later, when Harden got docked with a technical foul after getting tangled up with forward Matt Barnes with 5:27 remaining in the quarter. That added more fuel to the Clippers' tank as they went on an 8-0 run for an 87-68 advantage after two foul shots by Paul.

Houston put together an 11-2 stretch to cut the gap to 89-79 after a 3-point basket by Jones, but a trey by guard Jamal Crawford with 27.3 seconds remaining gave Los Angeles a 92-79 lead heading into the final period.

"Just thank God, man, because you know there (were) times where it just seemed like everything was going their way," Howard said. "But we pulled together. We just kept saying we're not going to quit, we're not going to give up, we done come too far just to end it like this, and we just kept fighting."

NOTES: Houston's bench outscored Los Angeles' 37-16. The Rockets also enjoyed a 60-41 rebounding edge, including a 15-4 difference on offensive boards. ... Rockets coach Kevin McHale said he would like to see changes in the intentional foul rule. "I just think you have to let people play a little bit," said McHale, who has had his players purposely foul Clippers C DeAndre Jordan in each game of the series. "I wouldn't mind seeing them change it where you can't (intentionally) foul in the first 14 seconds of the shot clock, you can't foul in the first 10 seconds, something so you can play and attack. Something to allow some flow in the game because it gets hard to watch that sometimes. Games take five hours."