The Serbian notched up his 22nd successive victory at the Australian Open after a 6-3 7-6 (2) 6-1 first-round victory over his unseeded Slovakian opponent.
I know that I haven’t played my best
Djokovic, who is the defending champion, faces Argentinian Leonardo Mayer in the next round as the 26-year-old bids to win the tournament for a fifth time.
“I was happy with my concentration,” Djokovic told ATP World Tour.
“I thought I was prepared well. Physically I feel great. I’m very motivated obviously to play my best.
“I know that I haven’t played my best, especially in the second set. But, look, also credit to my opponent who was playing really nice tennis from the baseline.
“I won many easy points with the first serves and had a high percentage of the first serves in.
“That’s something that makes me very encouraged for this tournament and for every next match.”
Later in the Rod Laver Arena, third seed David Ferrer edged into the next round courtesy of a 6-3 6-4 6-4 victory over Colombian Alejandro Gonzalez.
Eighth seed Stanislas Wawrinka was barely tested as he secured his progress after Andrey Golubev retired in the second set with the score 6-4 4-1 in the Swiss’ favour.
Also in the Hisense Arena, Pole Jerzy Janowicz took five sets to beat home favourite Jordan Thompson – the No20 seed won 1-6 4-6 6-4 6-2 6-1 following a thrilling 196-minute battle.
“I didn’t play my best tennis; I was far from it,” Janowicz said. “I knew I had to fight for every single ball. He’s a young player in his first Grand Slam tournament, so I knew he might feel a little bit of pressure.
“He had the chance to win the match. Maybe he was a little bit nervous.
“Luckily, after every single game, I was getting better. I was more confident with my groundstrokes. In the fourth and fifth sets I was playing pretty okay.”
Finally seventh seed Tomas Berdych secured a comfortable 6-3 6-4 6-3 win over Kazkhstan’s Oleksandr Nedovyesov in the Magaret Court Arena.
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