Julius Randle collected 18 points and 11 rebounds, Brandon Ingram scored 13 points and Larry Nance Jr. added 12 points and 14 rebounds for Los Angeles (22-55). Thomas Robinson had 12 points and 10 rebounds.
Mike Conley and Troy Daniels scored 20 points each for the Grizzlies (42-35). Brandan Wright chipped in 16 points, while James Ennis III scored 14 points and grabbed eight rebounds. Tony Allen and Zach Randolph had 13 points apiece.
Lakers forward Tarik Black (mild left knee sprain) also missed the game.
Tyler Ennis' basket with 1:39 left gave the Lakers a 99-97 edge and a tip-in by Nance with 1:07 remaining boosted the margin to four.
After a turnover by Ennis, Russell sank a pair of foul shots for a 103-97 lead with 57.8 seconds left.
A 3-pointer by Conley sliced the margin in half with 48 seconds remaining, but Randle made one of two free throws to put the Lakers up 104-100 with 29 seconds remaining.
Conley converted another trey with 16 seconds left to cut the deficit to one, but Ennis hit a pair of free throws with 11.6 seconds remaining for a 106-103 advantage.
Conley air-balled a 3-point attempt with six seconds remaining. Randle made both free throws to seal the win.
NOTES: Lakers rookie G David Nwaba, who scored a career-high 19 points off the bench in Saturday's loss to the Los Angeles Clippers, has been one of the team's surprises. "He's a winner. I think he really is. Every time he plays he sets the tone for us," Lakers coach Luke Walton said. Nwaba signed a multi-year deal with the Lakers on March 21. Before being called up to the Lakers, Nwaba averaged 13.9 points and seven rebounds in 38 games with the Los Angeles D-Fenders of the NBA Development League. Nwaba managed three points in 16 minutes against Memphis. ... The Grizzlies visit the San Antonio Spurs on Tuesday. ... The Lakers play at San Antonio on Wednesday.