The Australian Open champion fired 18 aces and saved two set points in the third-set tiebreaker to emerge with a 7-5, 4-6, 7-6 (9/7), 6-2 triumph.
He was already struggling physically when he sailed into the courtside seats in the Louis Armstrong Stadium in the third set, diving at full stretch for a ball.
"It was crazy a little bit when I arrived in the stand, because it never happened to me," the Lausanne native said.
"It was quite a bad fall, but I'm lucky I didn't have any big problem with that.
"I was already struggling physically, so was it was nothing from the fall — I think I was quite lucky with that."
Wawrinka said it was mental toughness that saw him through.
"I was accepting the fact that I was really down physically in the third set, that I was struggling a lot with cramping and everything," he said.
"But I wasn't complaining about that.
"I stayed positive with that, tried to find the solution how to relax mentally, how to be better, how to fight with him."
Wawrinka fired 75 winners, including 27 in the third set that surpassed Robredo's total of 19 for the match.
He rallied from 0-3 down in the tiebreaker, finally sealing the decider with a forehand winner and the breaking Robredo to open the fourth set.
"I tried to be a little bit more aggressive, tried to start again to take my forehand back, not only playing backhand," said Wawrinka, who broke Robredo again for a 4-1 lead.
"A few little changes that made a big difference at the end of the match."
Things turned testy early in the fourth as Wawrinka and Robredo exchanged words, although neither player cared to discuss the moment later.
"It's something that can happen in a match," Robredo said.
"I think he did something not nice, and I just told him if he had a problem today."
Wawrinka, too, said it was just a matter of two players trying to win.
"It's always the same when you play a tough match," he said.
"He did few things that I did not like it, but at the end of the day it's a tennis match."
Although it cost him a little early in the match as he struggled to find his rhythm, Wawrinka said his third-round win by walkover -- which left him idle for four days -- meant he'd be fresher for his quarterfinal.
"The good news is that I won that match," he said.
"I still had only three matches, so even if today was a really tough match I did save a lot of energy during the four days."
Besides, Wawrinka added: "When you win, it's always more easy to feel good after."