The Lakers, who closed the game on an 11-0 run, had a 105-104 lead after Marshall's big shot, with rookie Ryan Kelly hitting a pair of free throws with 9.4 seconds left to finish off the rival Celtics.
Marshall has played in only 12 games this season for the Lakers after his call-up from the NBA Development League.
Through that span, Marshall is shooting 45.4% from the field and a team-high 46.9% (23 of 49) from three-point range.
His season averages of 10.7 points and 9.1 assists a game include four, low-minute appearances before injury pushed him into the Lakers' starting lineup.
As a starter, Marshall is averaging 13.4 points and 12.4 assists in eight games.
Despite Marshall's play, the victory over the Celtics was just the second for the Lakers since he took over at the point.
Nash's return (back) is still questionable. Bryant (knee) is shooting for early February. Henry (knee) will be re-evaluated soon.
Point guards Farmar (hamstring) and Blake (elbow) are still a few weeks away.