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Rublev had cruised to his most dominant win of the year in the Round of 16 one day earlier, swatting lucky loser Timofey Skatov aside by a 6-1 6-1 scoreline in just 59 minutes.

The No.1 seed looked bound for the last four when he took the opening set of this match, only for Van Assche to fight back for an eye-catching 3-6 6-3 6-4 success.

A hard-fought break in game four of the second set, in which Van Assche failed to convert three break points before making his fourth count, proved the turning point.

That was part of an 11-game run in which eight went the way of the 22-year-old, who is now into his first ATP Tour semi-final.

"I'm very, very happy about the win today. It's the best win of my career so far," he said after the win.

"It means a lot to me. I love Portugal. I've played well here, so far in my career. It's a place that I love and to be in the semi-finals... it's a great step."

No.2 seed Luciano Darderi and No.4 seed Alexander Blockx are still lurking on the other side of the draw and could represent possible final opponents for Van Assche or Gaston.