NEW ORLEANS – James Harden never wanted a foul to be considered in the act of shooting more.

The Rockets had spent the season vexed by the rule change that eliminated continuation calls, no one as much as Harden. But with the Rockets down three in the final seconds and the Pelicans choosing to foul Harden before he could take a 3 to tie, Harden tried one more time to gather and shoot as he was grabbed.

He did not pull it off. He was awarded just two free throws and intentionally missed his second attempt, missing the rim entirely, as the Pelicans held on, 115-113, wasting a Rockets comeback with one last push and a final defensive stand.

The Pelicans had controlled the game most of the way with Anthony Davis scoring 27 points with 11 rebounds and DeMarcus Cousins scoring 15 points with 13 rebounds and 11 assists before he was helped off the floor in the final 12 seconds with an injury that seems certain to end his season.

"It's his Achilles," Pelicans coach Alvin Gentry said. "He'll get an MRI. We'll know the severity of it tomorrow. Just know that it's his Achilles.

"We're scared about it. All of our guys feel terrible about it."

When the Rockets found their 3-point touch, led by Chris Paul and Eric Gordon, they rallied.

The Rockets had come all the way back from down 21. With 3-pointers from Trevor Ariza and Paul, and a pass from Harden to set up Luc Mbah a Moute for a dunk, they tied the game with 2 ½ minutes left. But they still had to deal with the Pelicans' two-headed monster inside.

After Davis put in a pair of free throws, Cousins ripped the ball away from Mbah a Moute and set up Darius Miller for a corner 3.

Paul sank a pull-up jumper before Ariza knocked down another 3, to tie the game again. But then, the Rockets were out of stops.

After Jrue Holiday drove to a lefthanded floater in the lane, Harden missed from 20 feet with 43 seconds left. This time, the Rockets were out of stops. They did coax a miss out of E'Twaun Moore in the corner, but Cousins put in the rebound for a four-point lead with 15 seconds left.

Davis fouled Paul shooting a 3-pointer, and Paul put in all three free throws with eight seconds remaining to cut the lead to one. But after Miller was fouled, the Pelicans led by three with 4.1 seconds left, giving the Rockets a last chance to shoot for overtime.

Harden, however, could not get into his shooting motion in time.

The Rockets' hope to counter the Pelicans' muscle with 3-point shooting did not work out for most of the night while only Paul and Gordon could make their shots.

Trailing by 21 with less than six minutes remaining in the third quarter, the Rockets were not quite ready to pull the plug, but one more Pelicans run might have been enough for the Rockets to call it a night.

With that, the Rockets made the first sustained run of the night, getting stops when Davis cooled off for a few minutes and even putting in a few 3s.

The Rockets pieced together a 17-4 run late in the third quarter, with Paul scoring 10 points in the final 2:15 before the fourth quarter.

The Rockets were still struggling to find anyone else to knock down their usual shots. With the Pelicans up 10, Mbah a Moute ended and began the fourth quarter missing open 3s. But even when Gordon found his touch, hitting three straight from deep, each time he could only bring the Rockets back to seven.

Finally, the Rockets broke through that barrier, with Paul taking a steal to a layup and a three-point play, bringing them within four with eight minutes left. That gave him 30 points in 30 minutes, but in the next 31 seconds, he picked up his fourth and fifth fouls, forcing him to the bench.

Other than Gordon, the Rockets had not found a reliable scorer all night. But as Harden returned, the Rockets were in position to steal a win in a game that seemed on the brink of hopeless.

Other than a brief burst, they were still looking for their usual 3-point shooting touch. When they found it, they sent the game to the final 2 ½ minutes tied. After spending so much of the night unable to make shots or get stops, the Rockets had a last chance. The Pelicans, however, had answers, up to the point they fouled just in time.