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In the tournament held in Melbourne, Australia, world classification number 66 Murray and 159 number Kokkinakis faced each other.
Losing the first two sets 6-4 and 7-6, 35-year-old Murray won the next sets 7-6, 6-3, 7-5 in the game, which lasted 5 hours and 45 minutes and ended at 04:06 am local time, and made his mark in the third round.
The match was the second longest in the history of the tournament, after the Novak Djokovic-Rafael Nadal final in 2012, which lasted 5 hours and 53 minutes.
Murray, who played 5 finals at the Australian Open but could not win any of them, defeated Italian Matteo Berrettini 3-2 in the first round match that lasted 4 hours and 49 minutes.
Murray was paired with Spaniard Roberto Bautista Agut in the third round.