LOS ANGELES >> If any NBA franchise historically exemplifies winning ugly, it’s the Memphis Grizzlies, who trademarked “Grit-N-Grind.”

But among NBA teams at the moment? The Lakers don’t care what path they have to take to get there.

There was some grit, some grind and, yes, even some blood on Tuesday night, dripping from the tip of Anthony Davis’ nose after a second-quarter foul. But the Lakers (32-34) churned out a 112-103 win, fueled by defense and the step-up heroics of Dennis Schröder, Austin Reaves and Rui Hachimura, who each had 17 points.

Davis tied it together, as he has throughout a week’s worth of games without LeBron James or D’Angelo Russell. Behind his 30 points and staggering 22 rebounds, the Lakers marched into the West’s No. 9 seed, the highest perch they’ve had in the standings since starting the season 0-5. They improved to 7-3 since adding five new players after the trade deadline

It took a gutsy stretch of defense: The Lakers held Memphis without a point for three crucial minutes, forcing five one-shot possessions ending with a defensive rebound. Davis was central to the defensive effort (making up for seven of his own turnovers). After grabbing a board over Memphis’ rangy big man Jaren Jackson Jr., Davis dribbled down in transition to hit Hachimura at the rim.

Aside from Davis, Schröder was a key source of late offense, hitting a bank floater against Xavier Tillman, and a teardrop jumper off a kickout from Reaves. He was also the team’s top playmaker with nine assists; Reaves had seven.

Hachimura had one of his better games as a Laker, inserted in the closing lineup for his physicality against a scrappy Memphis team as much as his fast break speed.

The Lakers had to outlast 26 points from Jackson, as well as 16 points from point guard Tyus Jones. Desmond Bane, one of the team’s best shooters, was held to seven points and missed his first eight attempts from the field.

The Grizzlies have been in turmoil since the weekend, when a slew of news landed at once: Their star, Ja Morant, is taking time away from the team after an incident when he appeared to flash a gun on an Instagram video from a club in Colorado; backup big man Brandon Clarke was also ruled out for the season with an Achilles injury.

But with Jackson — who coaches voted over Davis to make his first All-Star appearance last month — and Bane, a draft steal for the franchise, the Grizzlies are making do with the firepower they have. A 51-point quarter against the Clippers on Sunday signaled just how dangerous one of the top teams in the West still is.

The Lakers continued to ail themselves on the injury report: D’Angelo Russell was a game-time decision, but still missed his sixth straight game with a right ankle sprain; center Mo Bamba was ruled out the day before, as was LeBron James who was excused from the game with his right foot injury.