Kyrgios brought an abrupt end to Federer’s hopes of winning a fourth Madrid trophy with a 6-7(2) 7-6(5) 7-6(12) victory.
Swiss maestro Roger Federer has now won titles in 19 different countries.
Djokovic and Williams barely break sweat, while Azarenka makes light work of Wozniacki.
Azarenka, who is yet to drop a set against Sloane Stephens, beat the American 6-3, 6-2.
Veteran digs into his reserves to steer his partner past Bhupathi-Myneni into the semis.
Devvarman lost in straight sets 6-3, 6-4 to Yen Hsun Lu at the 2015 Chennai Open on Tuesday .
Delhi swayed to Roger Federer’s tunes, as did his rivals on the Swiss’s IPTL debut.
Roger Federer annihilated Andy Murray 6-0 6-1 to seal top spot in Group B in London.
Novak Djokovic defeated Stan Wawrinka 6-3 6-0.
Czech returns with a win after losing first match at ATP finals in each of the last five editions.
Djokovic is seeking a 3rd consecutive title alongside the River Thames, one that would seal the world no.1 ranking.
Kvitova will attempt to overcome a losing record against Petkovic of Germany to give the Czech Republic a good start.
Swiss master has a chance to cap off a good year by reclaiming the No.1 ranking at the ATP World Tour Finals.
Murray will take on World No.1 Novak Djokovic for a semifinal spot after the Serbian beat Frenchman Gael Monfils.
Djokovic, who is in a race with Federer to end the season on top, quickly build the lead playing some aggressive tennis.