Bryant had 10 points on 5-of-18 shooting without visiting the foul line and Gasol added 13 rebounds for the Lakers, who were coming off a 3-3 road trip while Staples Center was readied for Sunday night's Grammys.
The Lakers have beaten the Hawks six straight times at home and won 19 of the last 22 meetings between the teams in LA.
The Lakers trailed by five points early in the third quarter, but turned the game around with a 15-1 run sparked by four straight points by Bryant and a dunk by Metta World Peace.
Bryant scored eight of his 10 points during the burst and Andrew Goudelock ended it with a three, giving the Lakers a 59-50 lead.
Their advantage was 59-51 going into the fourth and reached 17 points on a Gasol three that made it 81-64 with around 3 1/3 minutes remaining.
Andrew Bynum had 15 points and 15 rebounds for the Lakers while World Peace and Goudelock scored 10 apiece. LA shot 44 percent from the field and held Atlanta to 34.4 percent.
The Lakers had 17 turnovers -- Atlanta scored 21 points off them -- including 10 in the second half. They led 27-24 after the first quarter and 42-41 at halftime.
Up next for the Lakers is a home-and-home series with the Phoenix Suns this weekend. They will play in LA on Friday and in Phoenix on Sunday...Atlanta's five-game road trip also includes trips to Phoenix, Portland, Chicago and New York.