The Russian fourth seed is yet to drop a set in the WTA Premier event as she moved past the Spaniard 6-1 7-6 (7-3) in an hour and 40 minutes.
After bowing out at the last 16 of both the US Open and the Wuhan Open, the five-time major winner remains on course for a fourth WTA singles title of the year despite some stubborn resistance from the world number 18 in the second set.
Sharapova hit six aces in the match and won the first five games on her way to a comfortable opener but Suarez Navarro saved eight of nine break points in the second set to force a tie-break, before the world number four powered into the last eight.
She will face Angelique Kerber or Svetlana Kuznetsova, who play on Thursday.
Caroline Wozniacki was bundled out by Sam Stosur, with the Australian ensuring a hard-fought 6-4 7-6 (11-9) success to move into the third round.
The defeat puts a dent in Wozniacki's hopes of securing a WTA Tour Finals, after the Danish sixth seed lost to Stosur for the first time since 2010.
Wozniacki will now only qualify for the end-of-season event in Singapore if Angelique Kerber does not make the quarters and Ekaterina Makarova does not reach the final.
There was no such upset for third seed Petra Kvitova, as she proved too strong for home favourite Peng Shuai.
Kvitova, already secured a place at the Finals after winning her third WTA title of the year in Wuhan, made a poor start to Wednesday's match as she lost the first two games against the Chinese world number 24.
However, the Czech recovered to win through, with the help of a 100 per cent conversion rate of four break points opened up on Peng.
France's Alize Cornet made it three career wins from three against American Lauren Davis - moving through 6-2 6-1 up in just over an hour.
Davis double-faulted seven times and saved just one of six break points as Cornet progressed convincingly to set up a meeting with Stosur.