Dallas led most of the game, but Paul Pierce hit a three-pointer - just his second basket of the night - to tie it at 85 with 25 seconds to play. West, a former Celtic starting because Jason Kidd has been out with a back injury, dribbled the clock down to about 10 seconds before giving it to the reigning NBA Finals MVP.
Nowitzki cut to the basket around Garnett and picked up a foul from Brandon Bass while floating the ball into the basket.
"He was up tight on me, and I had to go to the basket," Nowitzki said. "I saw the clock go down, and I really didn't see it go in."
The Celtics had a chance to tie, but Rajon Rondo's pass to Ray Allen behind the three-point line was too low to handle and went out of bounds.
Rondo scored 24 points for Boston and Garnett had 16 points with 10 rebounds. Pierce finished with five points and Allen had nine for the Celtics, who have lost two straight since winning four in a row.
"This is his [Rondo's] team right now, until everybody else gets it going," Celtics coach Doc Rivers said. "We need him to be aggressive. We need him to be a scorer. And attack. That's a change, but that's what it is right now until everybody else gets it going, because they are not."
Brendan Haywood had eight points and 11 rebounds and reserve Jason Terry scored 18 points as Dallas won its third straight game - all without Kidd. Nowitzki also had seven rebounds and four assists as the Mavericks, who swept Boston last season en route to their first NBA title, beat the Celtics for the third time in a row.
In other games:
* At New Orleans, Kevin Durant had 29 points and 10 rebounds and the Oklahoma City Thunder beat the Hornets, 95-85.
Durant hit 11 of his last 14 shots after missing his first three. He took over in the third quarter, scoring 11 points in the first 8 minutes as the Thunder extended a two-point halftime lead to 12 points. The Hornets pulled within four early in the fourth, but never threatened after that.
Russell Westbrook had 22 points and seven assists, and James Harden added 14 points for Oklahoma City, which won its fifth in a row.
* At Chicago, John Lucas III scored a career-high 25 points filling in for injured Derrick Rose and the Bulls beat the Washington Wizards, 78-64, for their third victory in 3 days.
Lucas, starting for the first time in his 70-game NBA career, was at the point in place of MVP Rose, who was out with a sprained big left toe. Lucas played 45 minutes, had eight assists, eight rebounds and hit 11 of 28 shots.
* At Portland, the Orlando Magic had seven players in double figures while shooting nearly 60 percent on the way to a 107-104 win over the Trail Blazers.
* At San Antonio, Tony Parker hit four free throws late in overtime to help the Spurs beat the Houston Rockets, 101-95. Parker scored 28 points on 12-for-22 shooting and Tim Duncan had 17 points and 11 rebounds for San Antonio, 7-0 at home.
* At Denver, Danilo Gallinari scored 22 points, Arron Afflalo and Corey Brewer each had 19 points and the Nuggets beat the New Jersey Nets, 123-115. Andre Miller had 12 points and 12 assists and Rudy Fernandez scored 15 for the Nuggets.
* At Salt Lake City, Kobe Bryant scored 40 points and Andrew Bynum blocked Al Jefferson's shot with 1.9 seconds left in overtime to lift the Los Angeles Lakers to a 90-87 victory over Utah, ending the Jazz' winning streak at five. The win was the first on the road for the Lakers.
* At Indianapolis, Danny Granger scored 24 points to break out of a shooting slump in the Indiana Pacers' 96-84 victory over the Atlanta Hawks.
* At Toronto, Tyreke Evans scored a season-high 29 points, DeMarcus Cousins had 21 points and a career-high 19 rebounds and the Sacramento Kings topped the Raptors, 98-91. Isaiah Thomas scored 12 of his 20 points in the fourth quarter and Jimmer Fredette had 10 for the Kings, who recorded their first road victory in five tries this season.