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The 37-year-old Spaniard, who is the third oldest man to reach this stage at Queen’s Club, struck cleanly from the back of the court to reach his 47th ATP Tour semi-final after two hours and 26 minutes.

Rune reeled off five points from 2-4 to claim the second-set tiebreak and spark hopes of a comeback.

But Bautista Agut responded superbly, winning 14 of 15 points behind his first delivery in the final stanza to claim the victory.

“It means a lot, it means that I still really love the sport,” Bautista Agut said.

“I wake up every morning with 120 per cent of dedication. I’ve been doing a lot of work this year, but the results didn't show. But I’m very happy with how I’m playing this week.”

Bautista Agut saved a match point in his opener against Nuno Borges and rallied from a set down in his second-round match against Jakub Mensik.

A former world No.9, the Spaniard will face countryman Carlos Alcaraz in the last four.