Roger Federer arrived at the Australian Open without having played a match this year. He would have to play himself into form at the first grand slam of the season and he continued on the right track when he moved into the third round with a 6-1, 6-4, 6-1 victory over Filip Krajinovic.

Any rust still clinging to Federer’s game was not visible under the lights of Rod Laver Arena as he raced to a 5-0 lead in 15 minutes and maintained his level for three sets. Perhaps most importantly, he overcame a challenging second set.

Serena Williams into Australian Open third round after testy win Read more

“I’m very happy, it’s a great start to the season,” he said. “I’m feeling really relaxed out on court. You train hard and you hope it pays off and not that it was all for nothing this week. I’m happy, I’m still going.”

Novak Djokovic, after leading Serbia to the ATP Cup title in the second week of the year, is certainly not undercooked. The defending champion eased past Japan’s Tatsuma Ito 6-1, 6-4, 6-2.

Djokovic’s display highlighted one of his most underrated improvements in recent years: his serve. The defending champion won 93% of points on his first serve and his second serve speed has also increased significantly. Last year he averaged around 96mph compared to 105mph on Wednesday.

“That’s something I worked on in the off-season,” he said. “That’s one of the priorities I guess of the training sessions, trying to get that advantage of winning a lot of easy points on the first serve.”

Facebook Twitter Pinterest Novak Djokovic won 93% of points on his first serve against Tatsuma Ito. Photograph: Lukas Coch/AAP

The eighth seed Matteo Berrettini lost 7-6 (7), 6-4, 4-6, 2-6, 7-5 against Tennys Sandgren of the United States and the 18th seed Grigor Dimitrov was beaten 6-4, 7-6 (6), 3-6, 6-7 (3), 7-6 (10-3) by the 22-year-old American Tommy Paul.

Alexander Zverev, who has been struggling on and off the court lately, said donating the $A4.12m winner’s cheque from the Australian Open would make him the “happiest person on the planet”.

The 23-year-old German said after making it through to the second round, “I’ve said it a lot of times, I’m not a money-driven person. I play the sport because I absolutely love it. I play the sport because I enjoy playing on big stadium courts, I enjoy playing the toughest matches in front of an amazing crowd.

“If I win the Australian Open I will be the happiest person on the planet. I think that the $4m will be in much better use in the hands that know what to do with it, and know how to help others.”