The Swiss world number four had too much firepower for the 51st-ranked Czech, reeling off a 6-2, 6-3, 7-6 (7/3) win in just under two hours on Rod Laver Arena.
Wawrinka, who beat Rafael Nadal to win his first Grand Slam title in the 2014 Australian Open final, will face boom-serving Canadian Milos Raonic in an enticing round of 16 match on Monday.
Wawrinka's stylish one-handed backhand was again to the fore and it was behind 11 of his 45 winners, which also included 18 aces.
The Swiss, who won his second major title at last year's French Open denying Novak Djokovic a coveted calendar-year Grand Slam, broke Rosol's service four times.
"It's never been easy against Lukas, he's a tough player, but I started well, I was moving well, returning well and I like the court and its condition," Wawrinka said.
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"I am trying to improve, I am working hard, practising hard. There are many things I can do to improve.
"I think I am playing better than last year, but all the other players are improving as well, so it doesn't mean I am going to be better in the rankings, but I am focusing on myself and so far I am happy with my start to the year."