The 29-year-old Russian, a three-time winner in Paris, plans to retire after this tournament. He will face U.S. Open champion Juan Martin del Potro of Argentina in the second round.
"The way he is playing right now, I don't think I have a chance," Safin said. "I'm going to fight 100 percent. But to win it? I'm not sure."
Safin saved the match points by serving three aces when trailing 5-4 in the third set. He closed the match with a forehand volley on his first match point in the tiebreaker to improve to 24-4 at the Paris Masters, where he won in 2000, '02 and '04.
"It's probably the best way to save the match points," said Safin, who had 24 aces. "It's not as painful, and I don't have to run around on the court and just hope for the guy to miss."
He broke in the fifth game when Ascione double-faulted and took the first set with a backhand drop volley. After trading breaks in the second set, Safin saved three break points in the sixth game before hitting a forehand long to ultimately force a decider.
Safin, a former No. 1, captured the 2000 U.S. Open and 2005 Australian Open among 15 singles titles. In his best result this year, he reached the semifinals at St. Petersburg 10 days ago.
"The way I'm moving right now is not really the best in my career," Safin said. "It's tough to pick up the bags, to go to the airport, to stay in the traffic, flight, passport control, wait for the bags again. It's very heavy. So I'm happy this is over."
Tomas Berdych, the 2005 champ, beat French qualifier Vincent Millot 6-3, 7-6 (4) after serving 10 aces and breaking three times.
The 247th-ranked Millot wasted a 5-2 lead in the second set and his Czech opponent finished the match with an ace on his first match point. Berdych, ranked 20th, will next face 14th-seeded Tommy Robredo of Spain.
Viktor Troicki of Serbia benefited from Paul-Henri Mathieu's calf injury to advance and will face 13th-seeded Radek Stepanek. Mathieu, who reached the Hamburg final this year, failed to convert a set point and retired when trailing 7-6 (4), 3-0.
"It's a shame because it was very close and I had some good opportunities to break him," Mathieu said. "But I suddenly felt a pain in my calf after a run and it was difficult for me to keep going."
A two-time title winner this year, Montanes will next play defending champion Jo-Wilfried Tsonga. The Frenchman retired in the first round of the Valencia Open last week with a wrist injury but is confident he can play before his home crowd.
"I played [in training] earlier today and everything went fine," Tsonga told a news conference. "I'm happy to come back here. I have a lot of good memories."
Tsonga is one of the seven players who can still qualify for this month's eight-man ATP World Tour Finals in London. No. 7 Nikolay Davydenko and No. 8 Fernando Verdasco, a semifinalist last week in Valencia, are in the best position ahead of Robin Soderling, Fernando Gonzalez, Tsonga, Stepanek and Marin Cilic.
To qualify for the season-ending event, Tsonga must win this tournament again without facing Verdasco in the final.
"I will give it everything, and will go on the court to win," Tsonga said. "I have nothing to lose."