Djokovic put up a nice vengeance win against Murray in Dubai to start his year.
Rafael Nadal raced into the quarter-finals with a 6-1 6-1 victory over Paolo Lorenzi, while Marin Cilic overcame a second-set wobble to beat Borna Coric 6-3 2-6 6-3. In his win over Dudi Sela in an earlier round, Kyrgios confronted Sela's fans and was caught in a heated exchange with his opponent at the end of the game.
Kyrgios was pleased with his focus throughout the one-hour, 47-minute showdown that was played in front of a buoyant crowd that was rallying behind Djokovic. I knew I had to stay in the moment because I've been in situations where matches have gotten away from me, so I had to stay switched on the whole time.
Tournament director Richard Krajicek claimed Kyrgios favoured "his passion beyond his profession" - something that seems so alien to the mentality shown by the likes of Djokovic, Federer and Nadal. Djokovic fell in the Aussie Open to Uzbekistan's Denis Istomin, then didn't play again until this week. However, Djokovic handled the pressurized the tiebreaker easily to be awarded a match point to win the game.
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Another player who is struggling this year is Australian Bernard Tomic, who retired in the first set of his match against American Donald Young.
Nadal bounced back from a break down in both sets to defeat Nishioka 7-6 (7/2), 6-3.
Also on Tuesday, Ernesto Escobedo defeated Stefan Kozlov 6-1, 2-6, 6-0, in a duel between Americans and will play against Steve Johnson in the second round.
The third-seeded Cilic beat countryman Borna Couric 6-3, 2-6, 6-3 to reach the quarterfinals for the second tournament in a row.