Patrick Beverley’s key 3-pointer propels Rockets by Pelicans _lowres

New Orleans Pelicans' Norris Cole (30) drives around Houston Rockets' Dwight Howard, top, during the second quarter of an NBA basketball game Wednesday, March 2, 2016, in Houston. (AP Photo/David J. Phillip)

HOUSTON — After missing an astonishing 31 3-pointers in the game’s first 47 minutes, the Rockets made their last one count Wednesday at the Toyota Center.

Patrick Beverley hit a go-ahead 3-pointer with 51 seconds left to lift Houston to a 100-95 win over the New Orleans Pelicans.

Before Beverley’s shot, the Rockets were shooting an NBA record low 2-of-33 from 3-point range, but somehow only trailed by one point.

With an assist from all-star James Harden, Beverley drained the 3-pointer to put the Rockets up 97-95, a lead they would not relinquish.

New Orleans, which led by six points two minutes earlier, turned the ball over twice and missed several shots leading up to the decisive bucket.

“We come out here after every game and we talk about ‘Well, we are still in the playoff race.’ No we are not. We are not,” Pelicans coach Alvin Gentry said.

“What we are is a team that when we have an opportunity to do something, we don’t get it done. That is the bottom line.”

“We didn’t execute down the stretch. It is as simple as that. When you turn the ball over three straight times you aren’t supposed to win it.”

Harden scored 39 points, despite making only 1-of-8 shots from 3-point range, while Dwight Howard scored 16 and Beverley 15.

With the loss, the Pelicans (23-36) fell six games behind the Rockets (30-31) for the eighth and final playoff spot in the Western Conference.

The Pelicans made 14-of-36 shots from 3-point range, but could not hold the fourth-quarter lead.

Norris Cole led New Orleans with 21 points, while Dante Cunningham added 16.

“It was a tough loss tonight because we beat ourselves,” Cole said. “We gave ourselves a great chance to win and it is tough not to come up with it at the end.”

Pelicans forward Anthony Davis started Wednesday after missing Saturday’s loss against Minnesota because of a pregame toe injury.

He finished with 12 points and eight rebounds.

“We had some big turnovers and they went down and capitalized on our mistakes,” Davis said.

Despite the horrid effort from beyond the arc, the Rockets still outshot the Pelicans from the field 44.4 to 40 percent.

Harden made 11-0f-24 shots and 16-of-18 free throws to lead the effort.

“We’ve got to get to the bucket,” Rockets coach J.B. Bickerstaff said. “I think James does that so well.

“As quickly and crazy as this year has been, in tight moments we’ve been pretty good. So, as long as we keep the game close, we feel like we can do enough to get the win.”

The Pelicans led by as much as nine points in the third quarter, getting four 3-pointers from both Cunningham and Eric Gordon.

Houston outscored New Orleans 43-29 in the final quarter and a half, despite producing the lowest 3-point percentage (8.8 percent) by a team with at least 30+ 3-point attempts in NBA history.

In the end, it didn’t matter, as Beverley hit the biggest shot of the game.

“Yeah, (Harden) passed it to me and I was just trying to get it up and it went in,” Beverley said.

“Although we came out kind of slow form the 3-point line today, the big shot at the end was huge.”