Josh Smith finished with 16 points, going 7-of-9 from the field, and grabbed 10 rebounds for Atlanta. Smith also tied his season high with five blocks.
The Hawks benefited from the Grizzlies' usual slow start to snap a four-game losing streak and win for the first time without leading scorer Joe Johnson, who is out with a right calf strain.
Memphis lost its fifth straight.
"We knew the crowd was going to be excited because it was Pau's first game back," Hawks guard Tyronn Lue said. "By jumping on them early, it took the wind out of the crowd, and we were able to maintain the lead."
Gasol missed the season's first 22 games with a broken left foot. He started and played 17 minutes, scoring four points and grabbing three rebounds. The 7-foot All-Star looked tentative in his first action, not crashing the boards and not taking a shot during his first two 4-minute stints.
"He was definitely not himself," Pachulia said. "He hasn't played an NBA game in like nine months. I don't think he was 100 percent. That's what I felt on offense, on defense, both ends of the floor, and I just took advantage of it."
Gasol acknowledged he was rusty, and despite the rehab and conditioning, he has a ways to go to be game-ready.
"Well, it was hard. A little slower than usual, and your legs get real heavy out there," Gasol said. "I'm just happy I got through it. It's frustrating that I can't help my team anymore than I did."
Marvin Williams and Lue each had 13 points for the Hawks. Pachulia's 22 points matched his season high, while Claxton's 19 points and 11 assists were both season highs for him. It is the balanced attack Atlanta needs until Johnson, the league's third-leading scorer, returns.
"We've struggled since Joe has been out," Hawks coach Mike Woodson said. "You don't know in this league which guys will step up that are in uniform when someone else is not.
"When Joe is on the floor, the guys look to him. When he's not, guys are soul searching. We showed tonight, we could make it without him."
Atlanta put the game out of reach early in the fourth quarter with a 17-4 run, capped by Smith's layup for an 84-66 lead, the Hawks' largest of the game.
Gasol's return wasn't enough to inspire the Grizzlies to a good start. Memphis' 18.6 points is the league's lowest-scoring average in the first quarter, routinely putting Memphis in an early double-digit deficit.
The scenario was repeated against the Hawks, as Memphis missed 10 of its first 11 shots, leaving the Grizzlies with a 14-4 deficit midway through the opening period.
"We've just got to come out and have a better start," Warrick said. "That's definitely a key for us."
The Hawks led by as many as 12 in the half before carrying a 47-37 lead into the break.
Pachulia worked against Gasol and the smaller Grizzlies' frontline for 13 points in the half, as Atlanta shot 53 percent. The Hawks shot that percentage for the game.
Memphis, meanwhile, shot 37 percent, was 1-of-9 outside the arc and committed 10 turnovers, hardly an equation to mount a comeback.
"I don't know how to explain it," Memphis coach Mike Fratello said. "We can't keep coming back every night."
In the third quarter, Memphis tried to run its offense through Gasol a bit more, with little success. Despite the ineffectiveness of the offense, Memphis was able to cut into the Atlanta lead a bit, leaving the Hawks with a 67-60 advantage heading into the final quarter.
The game was a homecoming for Hawks C Lorenzen Wright, who played college ball at the University of Memphis and was with the Grizzlies for five seasons until signing with the Hawks during the offseason. ... Memphis entered the game with a six-game winning streak over the Hawks. ... Atlanta is headed home after playing seven of its last eight games on the road.