The world No 1 was ambushed at the same stage in Toronto a week ago by eventual champion Jo-Wilfried Tsonga.
But Djokovic made sure he did not commit the same error twice as he began a bid to win the only Masters 1000 title missing from his resume. But he was tested by his French opponent, who took Tuesday's contest into a final set.
"He's not going to give you too many unforced errors and free points, so I knew that," Djokovic said. "But I managed to get a win in the end, and that's what matters."
He ended on his second match point after more than two hours. Four-time Cincinnati finalist Djokovic improved his record over France's Simon to 8-1. He is playing the pre-US Open Masters tournament for the tenth time.
In the only other second-round match played, Australian Open winner Stan Wawrinka was broken while serving for victory but pulled out a win over German Benjamin Becker 6-3, 7-6 (7/5).