Tatum, who had been listed as questionable with a sprained ankle, scored 37 points with 13 rebounds and five assists, while Jaylen Brown contributed 31 points on 13-of-18 field shooting.
Doncic scored a game-high 42 points with eight rebounds and nine assists but gave up five turnovers, and was blocked by Tatum in the fourth quarter.
Tatum and Doncic went head to head in the final quarter after the Mavs closed to 117-107. The Celtics forward first dunked, then made two free-throws after being fouled by the Slovenian, before blocking Doncic's driving lay-up.
Brown drained a three-point attempt after Marcus Smart's assist and suddenly it was 124-107 and game over.
Smart had 13 points with nine assists, while center Al Horford hit four-of-four from three-point range in his 14 points.
The Celtics moved to an NBA-best 14-4 record with the victory, while the Mavs suffered their fifth loss in six road games to fall to 9-8.
Wiggins stars as Warriors get back to winning ways
All-Star Andrew Wiggins enjoyed a season-high game with 31 points including six three-pointers as the Golden State Warriors won 124-107 over the Los Angeles Clippers.
Stephen Curry scored 22 points, making four-of-10 from beyond the arc, with six rebounds and nine assists as the Warriors improved to 9-10.
The Chicago Bulls claimed another big scalp only a few days after ending the Celtics' nine-game winning run, with a 118-113 victory over the Milwaukee Bucks.
Chicago trailed 109-106 with 1:15 remaining before Coby White sunk two three-pointers to sink the Bucks, who gave up 19 turnovers for the game.