Novak Djokovic will have to come back on Monday to finish his fourth-round match with Hubert Hurkacz at Wimbledon.
The seven-time champion was leading by two sets 7-6 (8-6) 7-6 (8-6) when play was suspended due to the 11pm curfew.
Djokovic saved two set points in the first set and fought to win another tie-break in the second on Centre Court.
Andrey Rublev dived into the quarter-finals of Wimbledon
Seventh seed Andrey Rublev dived into the quarter-finals with an extraordinary shot to bring up match point against Alexander Bublik.
Rublev was in the middle of the baseline when Bublik hit what he, and everyone else on Centre Court, thought was a clean winner down the line.
But the Russian dived forward, got a racket on the ball and somehow floated it over the net as Bublik scratched his head in disbelief.
Rublev, who had been two sets ahead but was pegged back by his opponent from Kazakhstan, went on to seal a 7-5 6-3 6-7 (6-8) 6-7 (5-7) 6-4 win after one of the most entertaining matches of the Championships.
“It was the most lucky shot ever,” said the 25-year-old. “It was luck, nothing else. I don’t think I can do it one more time.”
Rublev, in the last eight at Wimbledon for the first time, was joined by fellow Russian Roman Safiullin, who became the lowest ranked male quarter-finalist here since Nick Kyrgios in 2014.
The world No 92 upset Canada’s 26th seed Denis Shapovalov 3-6 6-3 6-1 6-3.
He will face Italian sixth seed Jannik Sinner, who beat Daniel Elahi Galan of Colombia 7-6 (7-4) 6-4 6-3.