The Serbian took full control of the opening set during the early exchanges, before going on to take it without dropping a single game.
The second set was less predictable, with both players struggling to record holds during their service games.
Ivanovic looked to be heading for the victory when she was serving for the match at 5-3 in front. However, Pironkova kept herself in the contest with a break.
It proved to be a momentary lapse from Ivanovic though, as the 24-year-old broke straight back to book her place in the final eight.