The Hawks were trailing by 12 points starting the fourth quarter but mounted a comeback and outscored the Lakers 27-15 down the stretch.
Atlanta's Paul Millsap sank a 3-pointer with 35 seconds left to forge a 103-103 tie.
After Gasol missed a hook shot with 19 seconds remaining, Jordan Hill grabbed an offensive rebound and Millsap was whistled for blocking Gasol.
That sent the Los Angeles forward to the free-throw line, where he connected on both foul shots.
He then blocked a Kyle Korver jumper with 2 seconds remaining, sealing the Lakers' second win in four games starting the season.
Korver scored 22 points while Millsap and Jeff Teague combined for 28 points and 13 rebounds for the Hawks.