HOUSTON -- Two of the most efficient offenses in the NBA offered a wondrous showcase befitting their reputations on Thursday night before crunch time unfolded. Someone needed to get down in the muck and make a play that was not quite so pretty and pristine.

While James Harden produced a triple-double and Clint Capela recorded two critical baskets in the restricted area in the waning moments, it was the grunt work of P.J. Tucker that helped the Houston Rockets hold on for a 117-113 win over the Cleveland Cavaliers at Toyota Center.

The Rockets (9-3) went nearly seven minutes without a field goal after securing a 13-point lead on a Tucker 3-pointer with 8:02 remaining. That drought enabled the Cavaliers (5-7) to fashion a 13-1 run, with LeBron James kick-starting the rally with a 3-pointer and Jeff Green ending it with a pullup jumper.

However, when Harden and the Rockets appeared gassed, Tucker saved them.

Tucker recovered a Harden missed layup by hitting the floor and outworking everyone, feeding Harden a pass from his backside with Harden in turn tossing a pass to the rim that Capela finished with a dunk through a Green foul. Capela completed the three-point play for a 115-111 lead with 1:10 left. Capela added a second-chance basket with 10.7 seconds to play.

"The key was obviously what P.J. did for us on the offensive rebounds," Rockets coach Mike D'Antoni said. "We struggled a little bit because I think we got tired legs, obviously. They kept battling through it. P.J. got every loose ball on the ground."

Harden tallied a game-high 35 points to complement his 11 rebounds, 13 assists and five steals. But he wore down in the fourth, missing 7 of 8 shots while the Rockets shot 27.3 percent in the period. Tucker, who had 11 points and nine rebounds, including six offensive boards, and Capela (19 points, 13 rebounds) carried the short-handed Rockets when their offense faded.

"We could have had a couple dagger threes that we missed, but we did find another way to win the game," Harden said. "It's going to be a lot of games like this throughout the season and postseason."

James led the Cavaliers with 33 points and seven assists, though he committed nine of the team's 19 turnovers.

Green scored 27 points on 11-of-15 shooting off the bench for Cleveland, which shot a sparkling 55.6 percent but was outrebounded 45-26. Houston had 17 offensive boards.

"You've got to have those defensive rebounds, especially when you're coming from behind and trying to win on the road," James said. "It's just tough when they shoot 45 threes a game and then they go to the free-throw line as well. I thought we did a great job, defensively, but a couple of things just didn't go our way tonight."

Houston hit 16 of 46 3-point tries and added 36 free-throw attempts compared to the Cavaliers' 14.

After shooting a robust 51.3 percent in their 36-point first quarter, the Rockets appeared to seize control for good when they opened the second period 6 of 6 from the floor, including 4 of 4 from 3-point range. Eric Gordon drilled the final 3-pointer to complete his personal 12-point blitz and extend what was an 11-point lead entering the period to 53-36 with 8:31 remaining in the half.

Green initiated his individual assault immediately thereafter, scoring nine consecutive points to cut the deficit to eight. James re-entered the game and offered support, and with the Rockets committing 11 turnovers in the period, the Cavaliers fashioned a remarkable rally.

Green and James combined for 36 points on 15-of-17 shooting in the quarter, with Cleveland reclaiming the lead at 62-61 on the first of two Green free throws at the 1:00 mark. James added a dunk and a reverse layup and, once down 47-25, Cleveland led 67-65 at the break.

"I give credit to my teammates," Green said. "They were able to find me in transition and get some layups and free throws to get things going."

NOTES: With Cavaliers G Derrick Rose sidelined due to a left ankle injury, G Iman Shumpert made his second start of the season and first since Oct. 28 when he posted five points and two rebounds over 20 minutes at New Orleans. Shumpert produced seven points and five assists Thursday. ... For the third time in four games, the Rockets eschewed the traditional game-day shoot-around, with coach Mike D'Antoni strongly considering eliminating the practice altogether. Houston played with verve against the New York Knicks and Utah Jazz after skipping a shoot-around both days. ... Rockets F Luc Mbah a Moute was unavailable because of a left knee contusion.