Federer has won this tournament only once, back in 2011, and has not played here since 2015. Federer, 37, is a record 20-time Grand Slam champion and also holds the record for the most weeks spent at the No.
In the second the Swiss broke in the opening game and controlled the match from that point onwards as he went on to secure victory.
Makes everything look easier.
"Oh, stop that! That was ridiculous", said the commentator of Federer's shot. "(The) Perfect combination." Three-time ATP champion and former world No. 28 Sousa also underlined the importance of being mentally strong in today's tennis. I won but if he had won, it would have been absolutely deserved.
"I hope I play better than in Cincinnati because I really didn't play well", Federer said.
"I'm still struggling. It's kind of a flu".
Djokovic, who will return to world No.1 next week, had his personal best winning sequence of 30 consecutive sets ended as Cilic played nearly flawlessly aggressive tennis to draw first blood in a magnificent duel.
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The pair served out until the ninth game when Federer finally found the break.
Djokovic now has a 30-1 record since the start of Wimbledon with his only loss in that time coming against Greece's Stefanos Tsitsipas in the third round of the Toronto Masters in August.
Sock had made an unexpected return to form after a wretched year since his surprise Paris triumph but his renaissance ended when Thiem fought from a set down to take control in a tough two-and-a-quarter hour duel.
"When you are playing and you are losing sometimes, you just get a little bit frustrated and upset", said Khachanov, who has reached the last-four of a Masters for the second time after a semi-final run in Toronto this summer. "It means a lot for me because I didn't do too well in the previous years in this part of the season".
Yet it only prompted Djokovic to increase his focus and produce some supreme play to turn the tide and prevail 4-6 6-2 6-3.
The sixth-seeded Thiem next faces unseeded Karen Khachanov of Russian Federation in their first career meeting. "I told him to tell him to keep it down a little bit because he was going a little bit too much over the edge".
The only consolation for Cilic was booking a place in the ATP Finals in London later this month courtesy of Nishikori's loss.