The Polish pro, who ousted US Open champion Andy Murray in the third round, stumbled in the early stages of the contest after number eight seed Tipsarevic clinched the first break of serve.
The Serbian committed strong forehands and well-executed returns across the court, which ensured him the opening set, leaving Janowicz with an uphill struggle.
Despite a slow start, the Pole grabbed a break point at the first time of asking and managed to hold with a strong serve and secure yet another break to take full control of the court.
Tipsarevic struggled to come up with answers to his opponent's shots and was forced to relinquish the second set, leaving it all up to the decider.
The Serbian failed to regain composure and called on his doctor after struggling with a problem in his throat and after much deliberation the game was called off, which has given Janowicz a chance to reach the final in Paris.