Madrid: The Swiss world number two, a three-time winner of the tournament, was beaten 7-6 (7-2) 6-7 (7-5) 6-7 (14-12).

Federer, 33, took the first set on a tie-break but it is the big-serving Kyrgios who will now play John Isner.

Third seed Rafael Nadal, looking for a fifth Madrid title in his home country, beat American Steve Johnson 6-4 6-3 and will play Italy's Simone Bolelli.

"My problem was I couldn't return his first serve," said Federer, who won only 18 of 85 first serve return points. "It was just a horrible performance on the return. That's what cost me the match."

Britain's Andy Murray overcame Philipp Kohlschreiber in a second-round match that did not start until 01:12 local time (00:12 BST) on Thursday morning.

In the women's event, world number one Serena Williams saved three match points against Victoria Azarenka to reach the quarter-final.

Last year Kyrgios, then aged 19 and ranked 144th in the world, became the first man outside the top 100 to beat a world number one at a Grand Slam since 1992 when he defeated the formerly top-ranked Rafael Nadal at Wimbledon.