Victory in the two-hour meeting sent the second-seeded Croatian into a last-eight battle with Germany's Philipp Kohlschreiber, a winner over Ivan Dodig of Croatia 6-4, 6-2.

Cilic, the 2014 US Open champion, was out-aced by the 40th-ranked Muller, nine to eight in a match without a single break of serve.

Cilic was runner-up at the Ahoy stadium two years ago and with the injury pullout of French top seed Richard Gasquet is now considered a top title favourite at the event which was to have also featured Roger Federer, now recovering from last week's minor knee surgery.

The winner of 14 titles, Cilic said his level has been improving after playing and winning a pair of tough matches this week.

"I played better today than the first day," the world number 13 said. "This was a very close match -- two tiebreakers and no breaks.
"In the second I was returning better and got into his service game. But I had to stay mentally concentrated. I was also lucky in the tiebreakers."
The Croatian faces Kohlschreiber for the ninth time, having lost five previous meetings to the 32nd-ranked German.
"If you can have a couple of tough matches and get through them, you start to play better," Cilic said. "I've adjusted to the tight situations. I'm always glad to win matches like this."

In the first round, Spanish sixth seed Roberto Bautista Agut carried momentum from his weekend title in Sofia into his opening match as he defeated Portugal's Joao Sousa 7-6 (7/4), 1-6, 6-3.

Bautista Agut, ranked 17th, already owns two 2016 titles and improved his record to 13-2 since the start of the year. He next plays Czech Jiri Vesely.

Sousa saved a pair of match points before falling on a third.

"It was not an easy match," Bautista Agut said. "I had a bad second set,  but in the third I really lifted my level again.
"There were a lot of rallies and long points. I'm off to my best start of a season and I hope to keep it up," said the Spaniard.
"I've played well in my last matches and I want to continue like this and get as many wins as possible this week."

Jeremy Chardy beat Evgeny Donskoy 6-7 (9/11), 6-4, 7-6 (10/8) after the Russian was inserted into the draw as a lucky loser following the pullout of Gasquet.