Muster has not lost in 22 matches on clay this year in four tournaments. He had won 20 finals on the surface since 1990 and 26 in all. Muster also won at Monte Carlo in 1992.
The loss deprived Becker of a chance of his first professional clay-court title after 43 tournament victories on faster surfaces. It was Becker's third defeat in a final at Monte Carlo.
Becker was largely to blame for his own downfall. He earned his two match points at 6-4 in the fourth-set tie-break, but double-faulted on his first and then netted a forehand on the other, one of his 82 unforced errors. Muster had only 24 unforced errors in the three-hour, 16-minute match.
Becker appeared to have the match won after the first two sets before the errors crept in. "I had all the chances in the world," he said. "But he didn't give up."
"I don't know how I won the match," said Muster, who was barely able to finish his semi-final on Saturday because of dehydration. After more than 10 hours' rest the Austrian was cleared to play by doctors and had no problems. Instead it was Becker who faded.
Muster took the third set in 28 minutes, with Becker losing three of his service games. After Becker had squandered his two match points in the fourth-set tie-break Muster gained the set on a forehand winner and yet another Becker error.
In the 22 minutes of the final set, Becker lost his three service games and ended the match by hitting a service return out.