Zverev, 22, struggled with his timing initially against the mercurial Italian but with his opponent’s level fluctuating wildly he played solidly thereafter to win 3-6 6-2 6-2 7-6(5).
Blocking his path to a first Grand Slam semi-final will be the top seed and world number one Novak Djokovic.
“I didn’t start well and he did. He played very aggressively, hitting the ball very hard, which made it difficult,” Zverev said. “But then after the first set, I played three very good sets.”
Zverev played a dreadful service game at 3-4 in the first set, double-faulting twice then framing a forehand out to gift Fognini the break which he backed up by holding serve to love.
The German ranted at his watching father and coach and seemed in trouble again early in the second set.
Fognini threatened again at 2-2 but Zverev responded with a superb dipping forehand pass on breakpoint down. Two more double-faults offered Fognini another couple of chances to break, but Zverev fired down aces to save both.
It proved a turning point as Zverev suddenly focused on the job in hand and he broke the Fognini serve in the next game and then again to level the match.
Zverev seized on a Fognini drop shot to whip away a forehand and break serve for 3-1 in the third set and the Italian’s frustration boiled over in the next game when he smacked a forehand long and slammed his racket on to the court.
Fognini, who beat Zverev on his way to the Monte Carlo title in April, scattered his rackets then called for the trainer to have strapping applied to his right calf.
The errors mounted up and a double-fault ended the third set.
He was still a danger though and forced the fourth set into a tiebreak. Zverev went 6-3 ahead but wasted his first match point before Fognini belted a forehand winner on the second.
Zverev made sure on the next point as Fognini slapped a forehand wide.
Top seed and defending champion Novak Djokovic continued his untroubled progress as he beat Germany’s Jan-Lennard Struff 6-3 6-2 6-2 to reach a 10th successive quarter-final at Roland Garros — the first man to achieve that feat.
The Serbian, on course to hold all four Grand Slam titles simultaneously, has yet to drop a set this year and described the last two sets against Struff as “perfect”.
Things might be about to get tougher for Djokovic, though, with Germany’s Alexander Zverev up next after the fifth seed beat Fabio Fognini in four sets to equal his run in Paris last year.
Six of the top eight men’s seeds have reached the quarters. Eighth seed Juan Martin del Potro was beaten by the 10th seed Karen Khachanov, 7-5, 6-3, 3-6, 6-3.
Japan’s Kei Nishikori edged out home favorite Benoit Paire in five sets, having resumed two sets to one ahead after the match was suspended by bad light the previous day.
Paire served for the match in the fifth set but Nishikori scrambled over the line to earn himself the dubious honour of a meeting with defending champion Rafael Nadal who has looked in commanding form so far as he bids for title number 12.
French hopes in the singles were extinguished as Gael Monfils was handed a claycourt lesson in a three-set defeat by last year’s runner-up Dominic Thiem of Austria.
