Down by 10 points for most of the first half and with their backs against the wall, it seemed Italy’s wait for a first result under their new Argentine head coach would roll into Round 4.
But a yellow card for Jonathan Danty, later upgraded to a red after a bunker review, and a long-range penalty from Martin Page-Relo flipped the tie on its head.
Italy initially went further behind from a Thomas Ramos penalty after the break but were the more threatening team thereafter and stunned the Lille crowd after Ange Capuozzo’s converted try brought them level.
Paolo Garbisi had the chance to win the game with a kickable penalty at the death but after the ball slipped off the tee he rushed his kick as the shot clock ticked towards zero and the effort rebounded off the upright, denying Italy a memorable victory.
“It is a weird feeling," said Quesada. "Of course, having a draw in France is a hell of a result for us.
"But, on the other hand we know the boys did the job to win today and the way it finished is a pity, but I am proud of the boys and I think they will use this to keep on growing - it was a great game from our team."
"In the first half we had a couple of attacking balls and we lost the ball trying an impossible pass.
"We spent a lot of time defending, but those efforts were worth it as we didn't concede the points.
"It was about being patient and using the full width, luckily it was a big improvement from the last round."
After fighting back from 10 points down nobody would have begrudged Italy a first-ever away win over Les Bleus.
Only moments before his late miss, Garbisi nailed a far more difficult kick from the right touchline to bring Italy level but he was gutted that he could not see his side to a fairytale comeback.
“I was thinking about trusting my process,” he said.
"It is part of my job to put the kick over, I take full responsibility for that. I am sorry for the team and all the supporters - it is my bad and I will work on it.”
Quesada added: "Some kickers feel pressure, and I love those kicks as the team can have a reward, but I feel for Paolo Garbisi.
"I didn't see what happened because I was coming down the stairs. I saw him rushing and it is a pity, it would have been nice to have a historical win, maybe next time."
Having last tasted success against France back in 2013, this draw will still be looked back on favourably by the Azzurri.
They were without several key personnel, forced to turn to 22-year-old Riccardo Favretto and 21-year-old Ross Vintcent in the back row.
For Exeter University student Vintcent this was a near-perfect start to his Test career and if he continues to play with such maturity, nights delivering Domino's pizza for some extra cash might soon be behind him.
"I am very grateful for the opportunity to be playing in front of this many people and very grateful for this badge,” he said. “I am not saying the Domino's pizza shifts are over indefinitely that’s for sure.
"I think there is something brewing here and I am just very fortunate to be a part of it.
"It was tough out there, but I thought the boys dug in and defended well. We can be proud of the performance regardless of the result.
"We said at half-time, we are blowing, but they are blowing just as hard, so if we can just stick in the fight and go 80 minutes, we would put ourselves in with a chance and we did. It was just a pity about the last kick.”
Further dropped points for France, meanwhile, dealt their hopes of regaining the Championship crown a serious blow.
Defence coach Shaun Edwards believes his side were punished for their first-half profligacy but admits Italy were well worth their share of the points.
"We had the ball all of the first half, total dominance with territory and possession,” said Edwards.
“The second half was probably the total opposite. To be honest, to concede 13 is not too bad with 14 players, but we are very disappointed not to win.
"We want our team to score tries, we did have a lot of pressure. I think you do have to give credit to Italy, in their defence. They were on the goal line, getting underneath the ball. They were fantastic."
