Howard matched his season high with 27 points, six during a key fourth-quarter stretch, and Nowitzki added 21, including two free throws with eight seconds left, in the Mavericks' 108-105 victory over the Grizzlies on Saturday night.
"They were tough," Dallas' Jason Terry said. "They're a gritty team. We didn't play well tonight, but we came away with the win and are on to our next task."
Devin Harris had 19 points and eight assists to help the Mavericks remain perfect in five home games.
The Mavericks, who began the night with an NBA-leading free-throw percentage of 84, missed 12 of 40 foul shots but managed to hang on.
"We'll keep working on that," coach Avery Johnson said of the poor performance from the free-throw line. "We have really solid free-throw shooters, but since I mentioned our free-throw stats the other day, we've been going down."
Terry hit a 3-pointer and Howard scored six points during a 12-2 run that gave the Mavericks a 101-91 lead with 3:31 left.
But the Mavericks had a defensive letdown and the Grizzlies fought back with a 10-0 run capped by Miller's 3-point shot and his three-point play with 1:13 left that tied it at 101.
"We lost focus for a while but the guys stuck together," Howard said. "Miller's a great 3-point shooter. We should have been out there on him."
Nowitzki's basket with 1:01 remaining put Dallas ahead, Rudy Gay scored on the other end to tie it at 103, then Nowitzki connected on two free throws to give the Mavericks a 105-103 lead.
Harris stole the ball from Gasol on Memphis' next possession, and Harris converted one of two free throws for a 106-103 advantage with 17.5 seconds to play.
Harris' fifth steal of the night matched a career high, and it proved to be one of the biggest plays of the night.
"We scouted him before," Harris said. "He likes to spin and come back to his left. He just happened to have the ball out and I got a piece of it."
Juan Carlos Navarro's two foul shots with 10.2 seconds left pulled Memphis to 106-105.
Nowitzki's two free throws with eight seconds remaining extended Dallas' lead to 108-105, and Navarro missed two open 3-pointers in the final 3.5 seconds.
"I was alone," Navarro said. "I was just trying to find one good shot and make it. It was bad luck."
Grizzlies coach Marc Iavaroni said Navarro was the first option on the final possession.
"We got the open look," Iavaroni said. "I thought we caught [the Mavericks] there but it didn't go down."
Memphis lost its eighth in a row to Dallas, but the Grizzlies were competitive. Memphis was coming off a 120-118 overtime loss to New Orleans on Friday night.
"Anytime we come into this place, we compete," Miller said. "But I'm not going to say it was a moral victory because I don't believe in that."
Memphis was ahead by 10 points midway through the second quarter, but Howard's 3-point play triggered a 21-10 run over the final 7:20 of the second quarter to give Dallas a 54-53 halftime advantage.
Memphis C Darko Milicic was out with a badly sprained left thumb sustained early in the second half of Friday night's overtime loss to New Orleans. He'll be evaluated by team medical personnel on Monday. ... Dallas G Eddie Jones will be out for a few more games because of a sore right leg. ... G Maurice Ager started his second straight game for Dallas and will continue in that role for at least the next three games. ... Johnson recorded his 150th coaching victory in his 191st game, making him the fastest coach to 150 in NBA history. Runner-up Phil Jackson needed 203 games to reach 150. ... Nowitzki, who started the night with a free throw percentage of 82, missed his first four from the line. ... Memphis rookie G Mike Conley sustained a right shoulder strain in the third quarter and did not return.