The victory makes German Haas the oldest men's singles grand slam quarter-finalist since Andre Agassi at the US Open in 2005 and the oldest at the French Open for 42 years.
Haas said: "These are cool stats sometimes to hear and to know about. It makes you proud.
"But what I'm really proud of is that I reached the quarters here for the first time, not knowing if that was ever going to be possible."
The 12th seed has been dogged by injury throughout his career and two years ago dropped off the rankings altogether.
Last year he had to qualify for the tournament but he is now on the verge of a return to the top 10 for the first time since 2007.
The best match of the day on paper looked to be Stanislas Wawrinka against Richard Gasquet, and it certainly did not disappoint, with a combined 149 winners hit.
Wawrinka and Gasquet are two of the game's most stylish exponents and the Swiss eventually came through 6-7 (5/7) 4-6 6-4 7-5 8-6 in four hours and 16 minutes.
Gasquet has a terrible record in fourth-round matches at grand slams, having won only one of 16, while, of his last six five-set defeats, five of them have been from two sets up.
It was harsh on the Frenchman, who ran out of gas rather than heart, while Wawrinka, who now has to recover for a match against Rafael Nadal, has come back from two sets down at the French Open to win four times.