Mobley, a second-round pick from Rhode Island, was 7-of-11 from the field.
"He's a tough kid and a very skilled player -- a gamer," said Houston coach Rudy Tomjanovich. "He's also doing a very good job for us on the defensive end."
Mobley said he came into the league as an offensive player but knows "my first job is to play defense. I'm learning every day. Teams challenge me but I go right back at them."
The Rockets appreciate Mobley, a guard who is averaging 8.9 points and 2.4 assists.
"Mobley is doing a good job defensively," said Scottie Pippen. "Offensively we've given him a lot of freedom. He has a lot of confidence."
It was Houston's third consecutive victory and seventh in nine games. The Rockets also beat the Mavs for the 11th straight time.
Olajuwon did most of his damage in the first half while Mobley hurt the Mavericks in the second half.
Houston built a 61-46 lead on a basket by Mobley with 2:12 left in the third period. Mobley had eight points for the Rockets in the period and Olajuwon scored six.
The Rockets went ahead 73-57 with 8:18 to play before Dallas rallied and cut the deficit to 80-76 with 3:24 left on a basket by Gary Trent.
But Olajuwon scored on a dunk, and Charles Barkley made a jumper, two free throws and a dunk to end the threat. Barkley finished with 16 points and 11 rebounds.
"We knew Dallas would make a run," Barkley said. "The thing I like about this game is that we won. It doesn't have to be pretty."
Olajuwon was 10 of 18 from the field and hit all four of his free throws. He also had seven rebounds.
Dallas coach Don Nelson said he was surprised the game was as close as it was considering the Mavs shot only 35 percent.
"It was a nightmare game for us offensively," Nelson said. "It's amazing we got within four points considering they shot 50 percent and we shot 35 percent. Shawn kept us in the game."
Olajuwon hit 7 of 11 shots in the first half and scored 14 points as Houston took a 39-31 lead. Dallas shot only 29.5 percent in the half, including 0 of 8 by guard Steve Nash.
Nash finished 1-for-10 and was booed by the hometown crowd in the second half every time he touched the ball.
"They had every right to boo," Nash said.
The last Dallas win over Houston was a 117-114 decision at Reunion Arena in March 1996. Houston leads the all-time series 62-36, including a 105-95 victory earlier this year ... The Rockets are one win away from evening their all-time record. It's now 1,284-1,285.
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