But two finals, and five more semi-finals later he is still searching for that first victory.
None of those last-four places have come at Wimbledon, thus the grasscourt major seems an unlikely place for the German to break his duck.
But the fourth seed has at least extended his latest quest into the second week after surviving an injury scare and an epic third-set tie-break to beat Britain's Cameron Norrie and reach the fourth round.
The 27-year-old produced an impressive display of serving to win 6-4 6-4 7-6 (17-15), finally ending Norrie's rugged resistance by converting his sixth match point.
Alexander Zverev clutches his knee after falling in his match against Cameron Norrie at Wimbledon. (AP PHOTO)
Norrie had five set points of his own to extend the contest and ask questions of Zverev's knee which he appeared to strain when sliding and falling awkwardly early in the second set.
But Zverev, who reached the semi-final of this year's Australian Open and the final of the French Open, never wavered and Norrie cracked first on the 32nd point of the tiebreak, sending a shot over the baseline to end the duel.
Seven more points and it would have broken the Wimbledon tie-break record. That remains with Bjorn Borg, who played a 38-point tie-break against Premjit Lall in 1973
"I do feel like a cow on ice sometimes (on grass)," Zverev said.
Of his knee he added: "I feel restricted on some of the movements but I will check and see what it is."
Russian fifth seed Daniil Medvedev overcame unseeded German Jan-Lennard Struff 6-1 6-3 4-6 7-6 (7-3) in a match that was disrupted by rain.
American 14th seed and US Open semi-finalist Ben Shelton beat Canada's Denis Shapovalov 6-7 (4-7) 6-2 6-4 4-6 6-2 to reach the fourth round where the 21-year-old will face top seed Jannik Sinner.
When the match ended, Ben shouted over to his father and coach Bryan, who himself reached Wimbledon's fourth round in 1994, "We're back, Big Dog!"
French 16th seed Ugo Humbert beat another American, Brandon Nakashima 7-6 (11-9) 6-3 6-7 (5-7) 7-6 (8-6) to line up a tie with defending champion Carlos Alcaraz.
Giovanni Mpetshi Perricard, who gained a place in the main draw as a lucky loser, reached the fourth round with a 4-6 6-2 7-6 (7-5) 6-4 third-round win over Finland's Emil Ruusuvuori and will now play Lorenzo Musetti, the 25th seed from Italy.
Earlier, Andy Murray's distinguished career at Wimbledon came to an end when Emma Raducanu withdrew from their mixed doubles match due to a wrist issue.
"Unfortunately I woke up with some stiffness in my right wrist, so therefore I have decided to make the very tough decision to withdraw from the mixed doubles tonight. I'm disappointed as I was really looking forward to playing with Andy but got to take care," Raducanu said in a statement.
Raducanu is due to play her fourth-round singles match on Sunday against New Zealand's Lulu Sun, and she is cautious having undergone surgery on both wrists and one ankle last year, keeping her out for eight months.
However, Andy's mother Judy said on social media the news was "astonishing".
Elsewhere, former Wimbledon champion Vic Seixas, who was the oldest living grand slam champion, has died at the age of 100.
Seixas won the 1953 Wimbledon singles title and the US Championships — now the US Open — the following year.
He helped the US reach seven straight Davis Cup finals between 1951-57, all lost to Australia except 1954 when Seixas won one singles match and the doubles with Tony Trabert.
with agencies
