Earlier, fifth-seeded Mikhail Youzhny of Russia advanced to the second round, beating Sergiy Stakhovsky of Ukraine 6-3, 7-6 (7), while Potito Starace of Italy defeated Russian wild card Ivan Nedelko 6-0, 6-1.
The 12th-ranked Simon, who was making his debut at the event, trailed by a break in each set. He then broke Mannarino two times in the first set and evened it at 1-all in the second.
The 86th-ranked Mannarino, who is yet to win a title, broke in the ninth game to stay in the match and held his serve in the decider to close the match on his third match point.
The 97th-ranked Sela broke Dolgopolov twice in each set to hand the 16th-ranked Ukrainian his second successive early exit after Jeremy Chardy of France ousted him in straight sets in Moscow last week.
Youzhny, who won the tournament in 2004, broke early in each set. Stakhovsky, the winner here two years ago, managed to break back in the second for 2-all and then force a tiebreaker. Youzhny closed the match on his second match point.
"It was a tough match although I managed to break early in each set," Youzhny said. "Stakhovsky had a set point serving at 6-5 on a tiebreaker but I returned well."