Dallas matched a season low for first-half points and committed 16 turnovers, but Memphis got off to an even poorer start than the Mavericks.
"We got off to a slow start offensively, but defensively we were pretty good," said Jason Kidd, who had 11 assists and four steals for the Mavericks.
The Mavericks limited the Grizzlies to 38 percent field goal shooting and Dallas held a 49-38 rebounding edge.
"When you hold a team to no 20-point scorers, that's going to put you in position to win," Mavericks coach Rick Carlisle said.
The Mavericks were also able to get out and run, holding a 21-4 advantage in fast-break points.
"Once we got some stops, we really got our fast break going," Nowitzki said.
Dallas closed the first quarter with a 14-2 run for a 22-12 lead. The Mavericks got eight points, eight rebounds and three blocked shots from Dampier in the opening quarter, with Dallas scoring its first 16 points in the paint.
"I kind of kept us in the game there in the first half," Dampier said. "On nights when those jump shots aren't going in, we've got to have like a gang effort to go out there and rebound, and we did that. The first half I was able to get my hands on a couple [rebounds] and put it back so it was really a big difference."
Memphis opened the game 4-for-21 from the floor and didn't have a field goal over the final 6:13 of the opening quarter.
"We didn't come out with a lot of energy," Grizzlies coach Marc Iavaroni said. "We were random, we weren't getting into sets. We said we wanted to run them, but we didn't want to get into a random situation and take bad shots."
The Mavericks got a 3-pointer from Terry and a layup from Howard in the final 29 seconds of the first half for a 42-32 advantage.
Memphis had its lowest-scoring half of the season and Dallas matched its fewest first-half points, going 20-for-46 from the field.
"Our shooting was just terrible in the first half," Nowitzki said.
Dampier's three-point play gave the Mavericks a 54-39 edge in the third quarter. The Grizzlies never got closer than eight the rest of the way.
Memphis was able to pull to within 89-80 with 3:40 left, but Nowitzki answered with a three-point play to close out the Grizzlies.
Brandon Bass came off the bench to give Dallas a lift down the stretch, scoring all of his 11 points in the final quarter.
Dallas C DeSagana Diop didn't come close on two free throws in the second quarter. The first barely nicked the front of the rim and the second was an airball. ...The Grizzlies are 1-14 all-time in Dallas. Their only road win against the Mavericks was on Nov. 26, 2005. ...Dallas is 9-0 when holding an opponent under 90 points.