The defending champion Nuggets rallied from 13 points down in the fourth quarter to beat the hosts 105-102.
Mavericks star Luka Doncic hit a three-pointer with 25 seconds left in the game, while Irving sealed the win with a left-handed shot from 20 feet.
The defeat means the Nuggets drop to second place in the Western Conference behind leaders Oklahoma City Thunder.
Doncic had a game-high 37 points, while Irving scored 24 to help the Mavericks end the Nuggets' five-game winning streak.
Denver's Jamal Murray scored 12 of his 23 points in the fourth quarter to lead his team's comeback, but it was in vain.
The Mavericks are in seventh place in the Western Conference, where the top six teams in each conference are guaranteed a playoff berth and the seventh through 10th seeds advance to the playoffs.
In other action, Bam Adebayo hit a three-pointer from 30 meters at the final buzzer to lift the Miami Heat to a 104-101 win over the Detroit Pistons.
Adebayo totaled 20 points and 17 rebounds, while Duncan Robinson was the leading scorer with 30 points for the Heat, seventh in the Eastern Conference.
Robinson also became the fastest player in NBA history to make 1,000 three-pointers, reaching the mark in his 343rd game, seven faster than the previous record holder Buddy Hield.
The Milwaukee Bucks recorded an impressive 140-129 victory over the Phoenix Suns despite star Giannis Antetokounmpo not playing due to a knee injury.
Damian Lillard and Bobby Portis scored 31 points each for the Bucks, who are second in the Eastern Conference.
Sam Hauser scored a career-high 30 points, all on three-pointers, but suffered a sprained left ankle in the Boston Celtics' 130-104 victory over the Washington Wizards.
Jayson Tatum also scored 30 points as the Celtics won their fifth straight and improved to an NBA-best 53-14.
Meanwhile, Victor Wembanyama recorded 33 points, 16 rebounds, 7 blocks and 7 assists in the San Antonio Spurs' 122-115 overtime victory over the Brooklyn Nets.
Paolo Banchero's 29 points led the Orlando Magic to a 111-96 victory over the Toronto Raptors, while Dejounte Murray recorded a double-double with 21 points and 10 assists as the Atlanta Hawks beat the Los Angeles Clippers 110-93.
