The Lakers, heading for the playoffs without the services of Kobe Bryant, jumped past Houston into the seventh post-season spot in the Western Conference and will meet San Antonio in the first round.
Houston will face Oklahoma City to begin the playoffs.
Los Angeles went into the closing night of the NBA regular season with its playoff fate uncertain.
The Lakers, however, learned early in the evening they would be in the postseason when Utah lost to the Memphis Grizzlies.
Los Angeles then got used to playoff intensity in an entertaining game that was the last of the 1,229 regular-season contests played in the NBA.
Houston forced overtime when Chandler Parsons hit a 3-pointer just before the buzzer and a free throw by Parsons gave the Rockets a 91-90 lead in the extra period.
Gasol then started the key Lakers' run and Los Angeles clinched the victory on two free throws by Steve Blake with 10 seconds left.
Blake scored 24 points to lead the Lakers while James Harden scored 30 for the Rockets.