Gallinari, playing just his third game since missing almost two months with a partially torn left glute, finished with a season-best 28 points. Tobias Harris added 19 for the Clippers, who scored the game's final 13 points after trailing 101-91 with 4:42 to go.
The win was the Clippers' fourth in their past five games and 14th in their past 20.
Wesley Matthews had 23 points and Devin Harris 16 for the Mavericks, who missed their last seven shots and mixed in three turnovers in their game-ending scoring drought.
The last of Dallas' misses was a 3-point attempt by Matthews with 7.0 seconds left that could have given the Mavericks the lead.
Los Angeles' Avery Bradley completed the scoring with a layup in the final second.
Nowitzki's seventh minute of the game allowed him to become just the sixth in league history to play 50,000 or more minutes in their careers. He joined all-time leader Kareem Abdul-Jabbar (57,446), Karl Malone, Kevin Garnett, Jason Kidd and Elvin Hayes.
Nowitzki played 25 minutes and contributed 12 points and six rebounds to the cause. Along the way, he also passed Hayes, who played exactly 50,000 minutes in his career, for fifth place on the NBA's all-time list.
A 3-pointer by Matthews with 4:42 remaining gave Dallas a 10-point lead. However, the visitors never scored again en route to the sixth loss in the past seven games.
Gallinari and Lou Williams hit two free throws apiece to begin the Clippers' game-ending run. Williams then sank a jumper and Gallinari a 3-pointer to get Los Angeles within 101-100, setting up Gallinari's game-winning free throws.
Williams had 15 points, Bradley 12 and Sam Dekker 10 for the Clippers, who now get three days off before a reunion with recently traded Blake Griffin on Friday night in Detroit.
DeAndre Jordan grabbed a game-high 13 rebounds to complement six points for Los Angeles, which won the season series 2-1 over the Mavericks.
Dennis Smith Jr. and J.J. Barea had 12 points apiece for the Mavericks, who have not won a season series from the Clippers since 2011.
Dwight Powell collected a team-high 10 rebounds to go with eight points for Dallas, which played without leading scorer Harrison Barnes, sidelined due to a sprained left ankle.
--Field Level Media
Dallas | L.A. Clippers | |
Wesley Matthews 23 | Scoring | Danilo Gallinari 28 |
J.J. Barea 5 | Assists | Lou Williams 8 |
Dwight Powell 10 | Rebounds | DeAndre Jordan 13 |
Devin Harris 6 | Free Throws Made | Danilo Gallinari 6 |
J.J. Barea 1 | Steals | Avery Bradley 3 |
Wesley Matthews 2 | Blocks | DeAndre Jordan 2 |
Team | Points | FG% | 3PM-3PA | FTM-FTA | Assists | Rebounds | Blocks | Steals | Turnovers |
Dallas | 101 | 41.2 | 17-42 | 18-20 | 22 | 38 | 5 | 5 | 20 |
L.A. Clippers | 104 | 48.3 | 10-27 | 10-12 | 28 | 39 | 3 | 10 | 13 |