The German second seed had gone to bed the previous evening tantalisingly close to breaking new ground at Wimbledon, leading by two sets and 3-3 in the third when Wimbledon's strict 11 p.m. curfew halted his progress.
On the resumption, a listless-looking Zverev lost 12 of the first 13 points to drop the third set but managed to re-focus to win 6-4, 7-5, 3-6, 7-6(6).
Zverev double-faulted on a second match point in the tiebreaker but was spared further overtime as 13th seed Lehecka netted a backhand.
Huge serve and baseline power
His attempt to add the Wimbledon crown to his maiden Grand Slam title at last month's French Open will continue with a heavy-metal last-eight clash with American Taylor Fritz.
"Who would have thought it's only taken me 12 years to get (to my first Wimbledon quarter-final), but I'm incredibly happy and relieved. But of course I want to play three more matches."
The 29-year-old had reached the fourth round on three previous occasions but despite boasting a serve that can trip the speed gun at 140 mph and heavy baseline power, the German has never looked as confident on the lawns.
This year, buoyed by finally winning a Grand Slam title at the 41st attempt and with Wimbledon's courts firmed up by the hot sunshine, Zverev is finally looking comfortable.
The powerful Lehecka presented a huge test but after finally getting on court around 9 p.m. on Monday, Zverev produced a clinical display and almost beat the clock.
Re-energised by the interruption, Lehecka began in stunning fashion on Tuesday and within minutes he had won the third set.
Zverev went back off court before the start of the fourth set and re-established his rhythm on serve to keep Lehecka at bay. Zverev got ahead early in the tiebreak but at 6-5 he double-faulted to hand Lehecka an escape route.
Lehecka could not take advantage of his reprieve, though, as Zverev booked a Wednesday date with Fritz — a player he has beaten on two of their three Wimbledon meetings despite an overall losing record to the American.
Asked what can be expected, Zverev said: "I don't think it will be very entertaining because we both serve 140 mph and maybe there won't be many rallies."
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