The Serbian would have held on to his top ranking had he reached the final of the tournament in France, but now his fate is in Murray's hands as the three-time Grand Slam champion needs two more wins to overtake his rival.
The Croatian went a break up at the first time of asking in the opening set, but Djokovic, who has won the title in Paris four times, responded with a break point of his own.
After battling to hold serve and keep the set at 4-4, Cilic converted his second break point to take a one-set lead in 46 minutes.
The second set was a tight affair as both competitors saved two break points apiece before dropping serve, and Cilic looked as though he would wrap it up when he produced two match points, but Djokovic held to force the contest into a tie-break.
The 12-time Grand Slam winner drew first blood, but a double break nudged Cilic ahead and he went on to claim the breaker 7-2, setting up a semi-final clash against John Isner in the process.