With the temperatures soaring, the former champion fired a barrage of winners past the Latvian to roar through the first set in 23 minutes at Rod Laver Arena.
Sharapova wavered when serving for the match at 5-4, allowing Sevastova to drag the match into a tiebreak, but the Russian doubled down on her baseline firepower to raise three match points quickly.
She closed out the match on the second when Sevastova clubbed a forehand long and will next meet the winner of 2016 champion Angelique Kerber and Donna Vekic for a place in the last 16.
(Editing by Peter Rutherford)
