Gasquet rallied from a set and two breaks down to beat Jarkko Nieminen 3-6, 7-5, 6-2 after the Finn failed to serve out the match when leading 5-4 in the second set.
The fourth-seeded Simon won the title here in 2009 and improved his head-to-head record against Tipsarevic to 5-1. He broke the Serb in his first service game and then saved a break point in the 10th game before clinching the set when Tipsarevic netted a forehand.
The Frenchman then broke for a 5-4 lead in the second after winning a Hawk-Eye challenge on his fourth break point, as the replay system showed his forehand winner clipped the line.
"I think I couldn't do any better than that," Simon said. "Janko has been playing amazing tennis since last year. It's difficult to beat him."
Gasquet made a slew of errors to fall behind 4-0 in the second set against Nieminen before starting his fightback. When serving for the match, the Finn hit two straight double faults and a forehand error then allowed Gasquet to level the set at 5-5.
The Frenchman dominated after that, breaking twice more in the decider and clinching the win when Nieminen's backhand sailed wide.
"At 3-6, 0-4 I thought I was losing," Gasquet said. "I thought he was better than me. I was hitting bad. Not in a good shape. But it's tennis, sometimes it can change."