Djokovic grabbed the crucial third set break in the seventh game to prevail 6-3 4-6 6-4. Coming off a round of 16 loss in Toronto, the Wimbledon champion pulled out the crucial points when he had to.
Simon battled hard throughout, almost breaking back in the eighth game of the third, and holding off one match point, but eventually fell short and dropped to 1-8 in his career against Djokovic.
Earlier, Tsonga was brought back down to earth with a bump with a 6-1 6-4 loss in his tournament opener to Russian Youzhny.
The 12th-seeded Frenchman, whose victory over Roger Federer in the Toronto final was his fourth straight win over a top-10 opponent, including a win over Djokovic, offered little resistance as Youzhny advanced in 68 minutes.
“I just gave everything last week,” said Tsonga, who was unable to get any practice in on Monday due to rain.
“Before the match I believed I was able to play at the good level but on the court I realized that it’s going to be impossible and it was.”
Third seed Stan Wawrinka of Switzerland pushed through his evening second round contest with German qualifier Benjamin Becker 6-3 7-6(5).
The world number four and Australian Open champion won 82 percent of his first serves to take the match in 83 minutes.
Croatian 14th seed Marin Cilic breezed to a 6-3 6-4 first round win over Spaniard Feliciano Lopez, who lost to Federer in the Toronto semis.
British qualifier James Ward claimed his first ATP World Tour Masters win by holding on to beat Spain’s Guillermo Garcia-Lopez 6-2 3-6 6-1.
Other first round winners included Americans Robby Ginepri and Steve Johnson, Italian Andreas Seppi, Canadian Vasek Pospisil, Frenchman Julien Benneteau and ninth seed Ernests Gulbis of Latvia. (Reuters)