After another day of low cloud and drizzle at Roland Garros, the Swiss world number one had to wait until after 1900 local time to get on court and said it was a race against the clock to complete his victory.
"Conditions were shocking," a clearly ruffled Federer told reporters after needing six match points to close out the victory in rapidly fading light.
"I tried to get out of it as quick as possible. It's not so easy when you go into a match and you have basically one hour 45 or two hours to complete it. So it was tough."
After the 10-times grand slam winner outclassed 168th-ranked Ascione in the first two sets it looked as though he would be heading for his evening meal in quick time.
However, Ascione threw a spanner in the works in the third set with some inspired tennis to prolong the contest on Court Suzanne Lenglen.
Federer squandered two match points at 5-4 as he was broken for the first time and saw another three go begging in the tiebreak as Ascione battled back from 6-3 down.
Ascione had two points to take the match into a fourth set and a probable Thursday finish before Federer edged the tiebreak 10-8 at the sixth time of asking.
Federer, bidding for the only grand slam title to elude him after falling in the final last year to claycourt nemesis Rafael Nadal, said he was pleased that he would now have a day off, although it was a close shave.
"I know they want to get their match over and done with," he said of the schedulers.
"What I don't like is if they think that, okay, you know I'm the favourite, I should win this in straight sets, let's get Roger's match over and done with and then he's happy.
"What about if it doesn't turn out this way, you know? I'll be very upset. And I was already not too happy playing so late. You start stressing out because I could hardly see the ball."
Federer will face Italian Potito Starace in the third round.
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