The Knicks hadn’t been able to solve the Houston Rockets prior to Leon Rose.

Presto.

Helped by a morning shoot-around pep talk from the new president, who officially joined the organization Monday, the Knicks snapped their eight-game losing streak to the small-ball Rockets at the Garden with rookie RJ Barrett the hero in a 125-123 thriller.

Routed a week ago in Houston, the Knicks were led by Barrett’s career-high-tying 27-point explosion and his game-sealing, driving hoop with 7.6 seconds left.

The Knicks limited James Harden for most of the game, but he came on to finish with 35 points and left with respect for the No. 3 pick in the 2019 draft.

“Aggressive,’’ Harden said of Barrett’s outing. “I like it, especially as a rookie. He’s not timid at all. When you’re aggressive and confident in your game, you look good out there. [I want] him to continue to build his confidence and keep being aggressive, which he will, to be great.’’

Down by two, the Rockets had one last go at it, but Russell Westbrook missed a jumper from the free-throw line with Frank Ntilikina hounding him at the buzzer.

“I got the shot I wanted,’’ Westbrook said. “We can’t take games like this lightly.’’

Ntilikina said he knew Westbrook would get the ball.

“[The prior play,] Russ caught the ball and attacked the basket for a layup,’’ Ntilikina said. “My thought was to make him change direction and didn’t want him make an easy layup. It was a good shot for him, but he missed it.’’

Harden, who scored 61 in his prior Garden outing on Jan. 23, 2019, missed a biggie 30 seconds earlier when he blew a shot in the lane with his team trailing by one.

It came down to Barrett, who drove left on P.J. Tucker and scored on a running, lefty banker, putting the Knicks up by three as Rose applauded from his seat with 7.6 seconds left. Barrett finished 10-of-18 from the field.

Two possessions before, Barrett had thrown up an airball.

“From the time we started working with him in Las Vegas since summer league, he’s never wavered his confidence,’’ said Knicks interim coach Mike Miller after only his third victory over a winning team. “He wants to make plays. He has that in him. Some guys don’t. He does. He doesn’t worry about the last play.’’

Knicks power forward Julius Randle led the rebounding domination, finishing with 16 points and 16 rebounds. The Knicks outboarded Houston, 65-54.

“We played to our size and strength,’’ Randle said. “I told [Rose], ‘Congrats, you’re undefeated right now.’ A nice first day for him.’’

Rose sat in the usual management seats behind the visitor’s bench — next to GM Scott Perry, capologist Michael Arciero and longtime executive Jamie Matthews.

Former Knicks coach Mike D’Antoni carried a 7-0 record against the Knicks as Rockets coach before Monday.

At one point in the first half, the Knicks held a 21-point cushion, thanks in part to a monster first quarter from Barrett, who continued his hot hand from the prior game against Chicago. Barrett, who scored 17 first-half points against the Bulls, racked up 14 points the opening period against Houston and 19 by halftime.

The best part of Barrett’s output Monday was that it came from both the 3-point line and from snaking to the basket.

“It’s a good team that’s been on a run — that’s a big win, everyone was locked in,’’ said Barrett, who was 3-of-8 from 3-point range. “It’s a good way to start a week. I just wanted to score [on the final drive]. There was an opportunity and I took it.’’

Miller believes Barrett’s recent surge over the past week is due to his previously sprained ankle returning to 100 percent. The performance was made even sweeter with fellow Dukie and Giants quarterback Daniel Jones in the Garden stands.

With a buyout no longer an option for Wayne Ellington, who isn’t eligible for a playoff roster because he did not clear waivers by Sunday, the shooting guard came off the bench to pour in 15 points, all from 3-point range (5-of-8).

Ellington said wins like Monday’s confirmed his decision.

“I’m a guy who likes to finish what he starts,’’ Ellington told The Post. “We faced a lot of adversity and we’re still building as a team. I saw an opportunity to grow with these young guys. There’s a lot of things that went into it but I’m happy to be here to finish out the year.’’