Davis had given Dallas fans still fuming over the trade of Luka Doncic plenty of reasons to welcome his arrival, scoring 26 points with 16 rebounds, seven assists and three of the Mavs' 18 blocked shots.
But he pulled up in pain with less than three minutes remaining in the third period, departing with what the team called a lower body injury.
There had been no contact when Davis stopped short and put his hand to his groin, heading immediately for the sideline.
Davis, whose Mavs debut was delayed as he recovered from an abdominal strain, downplayed the injury after the game, saying it was "nothing serious".
"I'm fine," he said, adding that he felt "a little spasm" in his groin-quadriceps area and couldn't get it loose.
Even so, the injury will likely fuel the ire among some Mavs fans at the trade that brought Davis from the Los Angeles Lakers in exchange for Doncic - the 25-year-old Slovenian star who led the team to the NBA Finals last season.
Some gathered outside American Airlines Center before the game with signs calling for general manager Nico Harrison to be fired.
Nevertheless, Davis received a huge ovation when he was introduced and the cheers were even louder when he fed Daniel Gafford for an alley-oop dunk for the first points of the game.
Davis had 14 points on six of eight shooting in the first quarter with eight rebounds, three assists and a block as the Mavs surged to a 33-20 lead.
Dallas would push their lead to as many as 21 on the way to a 65-48 halftime lead, but the Rockets sliced the deficit to two points in the third quarter.
The Mavericks rebuilt the lead with a burst launched by two big three-pointers from reserve Naji Marshall.
Kyrie Irving, held without a basket on five attempts in the first half, drove for his first bucket and drew a foul for a three-point play that pushed the Mavs' lead back to 82-73.
They led 89-81 going into the fourth quarter and held on to hand the reeling Rockets a sixth straight defeat.
Elsewhere the Lakers, still waiting for Doncic to make his debut as he recovers from a calf strain, shrugged off the absence of superstar LeBron James - nursing a sore ankle - to beat the Indiana Pacers 124-117.
Austin Reaves, questionable to start with an elbow injury, scored a career-high 45 points. Rui Hachimura added 24 on his 27th birthday to help the Lakers win their fifth straight.
In Chicago, Jimmy Butler made a winning start to his career with the Golden State Warriors, scoring 25 points on his debut in a 132-111 victory over the Bulls.
The Warriors trailed by as much as 24 points early in the third quarter but a stunning Stephen Curry-inspired rally flipped the game on its head.
Curry rattled in 24 points in the third quarter as the Warriors outscored Chicago 42-25 to edge into a slender lead before closing out victory in the fourth quarter.
Curry finished with 34 points, including eight three-pointers, to lead Golden State's scoring.
The Oklahoma City Thunder extended their lead at the top of the Western Conference, dominating the second-placed Memphis Grizzlies 125-112dominating the second-placed Memphis Grizzlies 125-112 on the road in a statement win.
The Grizzlies took a fleeting two-point lead early in the first quarter but after that it was all Oklahoma City, with Shai Gilgeous-Alexander finishing with 32 points. Aaron Wiggins added 26 points and Jalen Williams 25.
In New York, Jayson Tatum erupted for 40 points as the Boston Celtics thrashed the Knicks 131-104.
Payton Pritchard backed Tatum with 25 points off the bench, shooting six of eight three-point attempts, as the Celtics improved to 37-16 to remain second in the Eastern Conference.