Marion connected on 14-of-19 shot en route to the career-high total and grabbed six rebounds for the Mavs, who claimed a second straight win.
The Timberwolves, who staged a furious rally after trailing 60-43 at halftime, had a chance to win it on the game's final play when Kevin Love set up for a 3-point try from the corner.
Marion whacked him across the arm on the attempt, causing him to miss, but no foul was called and the game ended despite Love's protests.
The T-Wolves star finished with 36 points and 11 rebounds for his NBA-leading 28th double-double.
Kevin Martin (19 points) and Nikola Pekovic (18, 10 rebounds) also reached double figures.