Azarenka, who is unseeded, defeated Strycova 6-4, 6-4 to continue her dominant run at this year's Australian Open. She will face 2014 finalist Dominika Cibulkova in the next round.
It was a scrappy match and Strycova did well to keep Azarenka off-balance. Strycova won the first seven points before the former world number one won the next seven.
In the second set both women were broken, but Azarenka pulled ahead when it mattered.
The Belarusian, who won the Australian Open in 2012 and 2013, has bounced back from a disastrous injury-plagued 2014 season.
After the match Azarenka said: "I would never want to compare (myself now to how I played when I won here) because I think the game itself progressed a lot and I do feel I played better than I was playing two years ago.
"(I'm working on) being more consistent, being more aggressive, really taking more my chances… so this always can get better. I mean, all aspects of the game I feel I need to get sharper still; match play, endurance."