Clippers clinch home-court advantage in win over Kings, 112-108

SACRAMENTO — The Clippers were fully aware that the home-court advantage was at stake as soon as they took the court Wednesday night against a Sacramento Kings team playing out the string of another porous season.

It took all the energy and effort the Clippers had to beat the energized Kings, 112-108, in what was perhaps the final NBA game at Sleep Train Arena.

By winning their seventh consecutive game, the Clippers will open the first round of the Western Conference playoffs against the Memphis Grizzles on Saturday at Staples Center.

BOX SCORE: Clippers 112, Sacramento 108

The Clippers and Grizzlies finished with identical 56-26 records, but L.A. gets the advantage by virtue of winning the Pacific Division.

The Clippers have won three of four games against the Grizzlies this season.

“Whew! Whew!” Clippers Coach Vinny Del Negro said after the game. “We knew it was going to be a battle. I’m just proud of the guys sticking together.

“We win the last seven and get home-court advantage. We stepped our intensity up overall.”

For the Clippers to get the win, it took Jamal Crawford scoring 13 of his 24 points in the fourth quarter, including two big three-pointers late.

Crawford has made 149 three-pointers for a single-season team record.

“I didn’t even know about it until last week,” Crawford said. “It’s just a credit to, not just me making them, but my teammates finding me and setting great screens and Coach drawing up some great plays.”

It took Chris Paul running the show with 25 points and 11 assists, and making a free throw with 7.3 seconds left for the final margin.

It took Chauncey Billups making four consecutive free throws in the final 15.6 seconds to finish with 17 points.

It took Blake Griffin playing through lower back spasms.

He scored on a dunk and tipped in a Ryan Hollins miss for a 107-102 Clippers lead with 23.8 seconds left.

“Having home court is great,” said Griffin, who finished with seven points and four rebounds. “Hopefully we play well at home and take care of business.”

The Clippers knew before the jump ball that Memphis had defeated the Utah Jazz earlier that night, meaning L.A. had to win if it wanted home-court advantage.

But the Clippers knew the game against the Kings wasn’t going to be easy, not with the city of Sacramento doing all it could to keep the team and not have it relocate to Seattle for next season.

Sensing that this could be the last game in Sacramento, the crowd was enthusiastic, doing all it could to push a Kings team with the third-worst record in the West to play its best.

DeMarcus Cousins had 36 points, a career-high 22 rebounds and three blocked shots for the Kings to push the Clippers to the limit.

The Clippers’ 11-point, fourth-quarter lead was sliced to two points, but they stayed the course to pull out the win.

“It was a good team win for us,” Del Negro said. “It was a total team effort.”

broderick.turner@latimes.com

Twitter: @BA_Turner