New Orleans battled from behind throughout the game and closed within three points when Marco Belinelli made two free throws with 3 seconds left.
Gasol was immediately fouled and, needing to make only one of his free throws, he hit the first one to ensure the Lakers' third straight win.
Kobe Bryant led the way with 25 points, hitting 10-of-19 attempts from the field. The Lakers shot 50 percent overall. Gasol added 21 points and Andrew Bynum had 17.
New Orleans was led by David West with 23 points and 12 rebounds. Los Angeles defeated the Hornets for the fifth time in six meetings.
Bryant passed Oscar Robertson to take over ninth place on the all-time NBA scoring list.