The Australian Open champion eased past the Croatian 6-0 6-2 on Tuesday with just 46 minutes on the clock.
"I practised perfectly before," Wawrinka, who is seeded third, told the ATP's official website. "I expected a more difficult or more complicated first round against him. But I was able, as I said, to practise well before.
"I felt good on the court. I know that physically if I feel good, then I am able to put a lot of pressure on the opponent."