Tipsarevic is ranked No. 8 and was the only top-10 player not to have won a tournament this year. The second-seeded Monaco was seeking his third title of the year.
Tipsarevic surrendered a 4-1 lead in the second set after a brief rain delay. He also dropped his serve after a longer, 20-minute interruption in the third. But he won the next two games on Monaco's serve to capture his first title on clay.
"I really still don't believe I won the tournament," Tipsarevic said. "But I kept fighting until the end."
The Serb was in control of the second set after winning seven straight games, wasting a break point that could have given him a 5-0 lead. With the score 4-1 in his favor, Tipsarevic insisted on stopping play after a few drops of rain.
The players never left the court but when play resumed after a few minutes, Monaco was a different player. He won 12 of the next 13 points, including all eight on Tipsarevic's serve. The Argentine then won the second set on a tiebreak.
Tipsarevic broke serve first in the third but another downpour sent the players to the locker room for 20 minutes, with the Serb down 30-0 on his serve.
When they returned, Tipsarevic again dropped his serve at love. He then broke back immediately, and took the match after Monaco sent a forehand into the net on Tipsarevic's second match point.