Atlanta's win streak matched its longest, which came in the first month of the 2016-17 season.
Houston lost its 17th straight game, tying the franchise record by the San Diego Rockets in the team's inaugural 1967-68 season. The Rockets haven't won since Feb. 4.
Atlanta led 73-58 at the half, but Houston won the third quarter 34-20 to pull within 93-92 entering the fourth.
The Hawks were without starting and backup centres Clint Capela (heel) and Onyeka Okongwu (adductor). Without their main two big men, the Hawks started power forwards Gallinari and John Collins.
Gallinari hit 5 of 8 from 3-point range and has scored at least 20 points in four of his last five games after reaching that mark just twice in his first 23 games this season.
Collins scored 20 points, and Trae Young had 13 points and 14 assists. Five Hawks scored in double figures by halftime, and six scored at least 10 in the game.
Victor Oladipo led Houston with 34 points, Jae'Sean Tate had 25, and Kevin Porter, Jr., scored 22.
The Rockets were without a slew of players, including Christian Wood, John Wall, Eric Gordon, P.J. Tucker and Ben McLemore. Houston played with the league-minimum eight players, including two players on two-way contracts and one on a 10-day contract.
Hawks: Capela, who was traded last February from Houston to Atlanta, received a highlight tribute video and was given an ovation by the Toyota Center crowd during a timeout in the first quarter. ... Without their big men, the Hawks were narrowly outrebounded 38-37.
Rockets: Houston is hopeful Wood (ankle) can return Wednesday against the Warriors. The Rockets have gone 0-17 since his injury. The Rockets are also hoping for a Wednesday return for Danuel House Jr., (right knee contusion). Wall (left knee contusion) is hopeful for a Friday return.
Hawks: Atlanta returns home to host the Thunder on Thursday night.
Rockets: Houston hosts Golden State on Wednesday night.