The 27-year-old Russian was on court for 69 minutes in registering a 6-1 6-3 triumph over the world No 17.
Sharapova broke serve four times in a one-sided opening set and, at one stage during the contest, won nine out of 10 games.
Sharapova dominated her opponent???s second serve but, despite the comfortable win, admitted giving the No 7 seed plenty of respect.
Suarez Navarro had beaten Sharapova in Montreal during the 2014 north American hardcourt season and the five-time Grand Slam winner said: “I’m always a little bit aware of girls that I lose to.
“I certainly know that she’s capable of playing really well. She plays defence great and makes you hit a lot of balls especially on a slower court like here.
???You just don’t want to give her that much time to play her game. I thought I did a good job of that today.
“Maybe I made a little too many unforced errors in the beginning but I finished strong.”
Sharapova has conceded just five games in her two matches in Brisbane so far.
She now faces 20-year-old Ukrainian Elina Svitolina who recovered from a set and 0-3 down to beat No 3 seed Angelique Kerber 4-6 7-5 6-3.??