Terry scored 31 points, and Dirk Nowitzki added 24 points and 12 rebounds in the Mavericks' 96-86 victory over the Rockets.
Howard, the Mavs' second-leading scorer, was inactive because of a left ankle injury. Yao, Houston's top scorer, missed the game because of a sore left foot.
Terry immediately made up for Howard's absence, hitting his first seven shots and scoring 18 points in the first half. He started his big night by sinking his first shot 9 seconds after coming off the bench in the first quarter.
"When the coach calls the first play for you and the shot goes in," Terry said, "you're like, man, it must be my night. And you try another one."
Jason Kidd had eight points, nine rebounds and seven assists for the Mavericks, who have won three in a row and 11 of the last 14 meetings with their in-state division rivals.
Tracy McGrady scored 16 points and Ron Artest added 14 for the Rockets, who shot 37 percent (29-of-78) from the field, including 6-for-25 from 3-point range. McGrady and Artest, both nursing injuries, each went 5-for-14 from the field.
"Throughout the game, we had some easy shots," said McGrady, hobbled again by a sore left knee. "Our offense was there, but we had some shots and we didn't make them."
Without Yao to anchor each possession, the Rockets looked disjointed all night and shot 35 percent through the first three quarters.
"When you don't have Yao, you've got to move the ball and you have to create situations," Houston coach Rick Adelman said. "We don't have a lot of guys who can break you down off the dribble."
Houston was lucky to only trail by 11 after the third quarter, and backup point guard Aaron Brooks hit two 3-pointers early in the fourth to help the Rockets pull within three.
But Terry hit a short jumper, Kidd swished a 3 and Terry converted a three-point play after McGrady's miss to restore Dallas' double-digit cushion.
The Mavs didn't find out until just before tip-off that Howard was out. Kidd said that didn't change their game plan much.
"We just kept going," Kidd said. "Whoever takes the floor has to step up and Jet [Terry] was big. The guys coming off the bench were huge for us."
Dallas started the final quarter 5-for-18 from the field, but Terry hit a 3-pointer with 1:58 remaining to put the Mavs up 88-79. Rafer Alston hit two free throws before McGrady hit a 3-pointer with 1:15 left to cut it to 88-84.
Terry answered with a drive down the lane and Nowitzki tacked on two free throws to clinch the Mavericks' fourth straight win at the Toyota Center. Terry finished 13-for-21 from the field, including two 3-pointers.
"It's a good shooting arena," he said. "I've heard others say it wasn't, but one man's trash is another man's treasure. I like the red background. It's like a bull's-eye to me."
It sure wasn't for the Rockets in this one. They missed five of their first six shots and trailed 10-2 four minutes into the game.
The Mavericks, meanwhile, sank 12 of 16 shots in the first quarter and led 31-25.
Terry scored the Mavs' first seven points of the second quarter. He finally missed, but then promptly stole the ball from Brent Barry and went in for a layup to put Dallas up 42-31.
Dallas was shooting 68 percent (21-of-31) with 3 minutes left in the half. The Rockets were shooting only 44 percent (16-of-38) after McGrady missed an alley-oop dunk off a feed from Alston.
"We didn't have good movement," Adelman said. "And if we did get shots, we didn't make them."
Dallas led 53-46 at the break and started the third quarter 2-for-8. But the Rockets missed their first seven shots and quickly trailed by 10.
Alston ended Houston's field-goal drought with a drive with 6:13 left in the third quarter to cut the Mavs' lead to 59-52. With no Yao to block him, Nowitzki answered with two turnaround jumpers over Luis Scola.
Dallas led 72-61 after Houston had its worst shooting quarter of the season, going 2-for-17 from the field.
Dallas coach Rick Carlisle said Howard was "day to day." The Mavericks play Memphis on Friday night. ... Yao underwent tests on his foot Tuesday and Wednesday that revealed no structural damage. "It's nothing bad," said Yao, averaging 17 points. "I'm all right, actually. I'll maybe take a few days, maybe one day." ... Artest played with a sprained right ankle.