The two former world number ones met in the final of the tournament in Auckland at the start of this year, with Ivanovic the victor on that occasion, but Williams ensured there was no repeat in Dubai as she brushed aside the Serbian 6-2 6-1 in just 56 minutes.
Having landed back-to-back titles in 2009 and 2010, Williams has been unfit to play at the tournament in the last three years, but the 33-year-old stretched her winning run in Dubai to 12 matches in seeing off Ivanovic, who she has now defeated in nine of 11 career meetings.
"I'm just trying to play well every day, take one point at a time and learn from my mistakes every match. I'm trying to go out there relaxed with a clear mind," Williams said on wtatennis.com.
"I definitely learned a lot from the last time we played each other. I definitely think I approached this match differently."
Another former Dubai champion also progressed to the quarter-finals as Denmark's Caroline Wozniacki saw off qualifier Annika Beck 6-4 6-4, but there was no such joy for the 2012 champion and second seed Agnieszka Radwanska, who was out of sorts amid blustery conditions as she lost 6-4 6-1 to qualifier Flavia Pennetta.
Radwanska said: "I didn't really feel the ball today at all. I think she was using the wind much, much better than I did. The conditions for me are tough. When I don't feel the ball, it's not good."
It was a day of shocks in Dubai with third seed Petra Kvitova also crashing out, losing 1-6 6-4 7-6 (7/4) to Carla Suarez Navarro, while the fourth-seeded Sara Errani was ousted 6-2 5-7 6-1 by Sorana Cirstea.
Fifth seed Jelena Jankovic is safely through to the last eight, however, as is Alize Cornet.