The Russian has now lost just five games en route to the last eight in Melbourne.
She established her superiority early on, taking her chance in the third game with a ripping forehand after Flipkens had double-faulted to set up two break points.
A marathon game then ensued on Sharapova's serve lasting 12 minutes, but the 25-year-old managed to hang onto her serve.
There was no stopping her from then on in, as she blasted her way into the lead.
Flipkens was powerless to prevent Sharapova from serving up yet another bagel - her fifth of the tournament - in the second set.