Though Nadal is the overwhelming favourite to proceed to the Round of 8, Schwartzman could prove to be a tough opponent for the Spaniard. I somehow just hung in and got a couple looks.
Eventually, the Bulgarian was able to survive the power serve of Kyrgios and take the victory 7-6 (7-3), 7-6 (7-4), 4-6, 7-6 (7-3). Cilic has only beaten Nadal once in six attempts.
Madison Keys advanced to the quarterfinals with a 6-3, 6-2 win over eighth-seeded Caroline Garcia.
Federer is now the only man left in the tournament not to have dropped a set, and Nadal will be relieved to have survived this test.
Kyrgios twice had 0/30 on the Dimitrov serve in the second set but it was the O2 champion who broke first and then had the chance to serve it out. Schwartzman had good looks on a couple of chances but two loose forehands long, along with a Nadal victor brought it back to deuce.
"I hope that it fills her with hope, strength and inspiration for the road ahead!", Kyrgios wrote on Facebook.
The prime-time clash crackled with intensity from the get-go with Dimitrov's elegant style contrasting with the explosive shot-making of maverick 17th seed Kyrgios.
His hammering of Murray at Wimbledon in 2014, in the quarter-finals, should have been the launchpad for Dimitrov to go on and consistently challenge in the championship matches at the majors. It gives me good confidence, good excitement on the court, when you are winning the matches, it just pushes you a little bit more, knowing that you believe in the things that are working.
Dimitrov has not won a major, coming closest in Melbourne previous year before losing a semifinal to Rafael Nadal in five sets, but he is enhancing his credentials as a next-generation champion. "But being honest, too, moments like this helps to be more confident in yourself, in your body". Paes and Raja suffered a straight-set defeat at the hands of the Colombian pair of Juan Sebastian Cabal and Robert Farah 1-6, 2-6.
Such was Wozniacki's confidence she even produced a between the legs "tweener" during the first set and although it did not win her the point it summed up her mood.
The early warning signs were there for the Spaniard, and Schwartzman showed his steel in an 80-minute second set. Sometimes try to do long points; sometimes short points. And after Nadal blew three break leads, Schwartzman made him pa taking the tiebreaker. The missed opportunities came back to bite Schwartzman, being broken in the next game. "That's the way I have approached it, one match at a time, and I continue to do that".
The world number 49 will face Grigor Dimitrov for a place in the last four, and Trevor Loten, who was Edmund's tennis teacher during his time at Pocklington Prep School, believes his former pupil has all the attributes to improve as a player and eventually take the mantle as British number one in years to come.
The combatants embraced warmly at the net after Dimitrov clinched a quarterfinal berth.