The critical victory kept the Lakers a half game in front of Utah for the final post-season berth in the Western Conference. Utah kept pressure on Los Angeles by defeating New Orleans earlier in the evening.
Gasol's layup gave the Lakers an 85-84 lead and the game's only other point came when Dwight Howard made the second of two free-throw attempts with 4.1 seconds to play.
Mike Conley then missed a driving layup in the final second that would have forced overtime, leaving the Lakers with their third straight win.
Kobe Bryant made only 10-of-23 shots, but scored 24 points to pace the Lakers. Gasol added 19.
Memphis got 21 points from Conley, but had a four-game winning streak halted.