The Russian won 6-1 6-0 in 68 minutes and has now dropped just five games in her four matches in Melbourne.
Belgian Flipkens was simply outclassed as Sharapova eased into a rematch with countrywoman Ekaterina Makarova.
The pair met here at the same stage 12 months ago with Sharapova winning 6-2 6-3.
Sharapova said: "I'm certainly happy to be playing this well but it's the quarter-finals and it only gets tougher from here."
The second seed's progression to her 18th career grand slam quarter-final was never in doubt.
She broke for a 2-1 first-set lead and never looked back, further breaks in games five and seven handing her a one-sided first set.
Her intensity did not drop in the second either, denying Flipkens a game as she followed up her thrashing of Venus Williams with another dominant display.
Watch: Sharapova cruises into quarter-final... More Videos