Second on the Road To Singapore leaderboard and seeded fifth this week, Black and Mirza were two points from defeat against Martina Hingis and Sabine Lisicki in their opener on Monday but had an easier time of it against Daniela Hantuchova and Mirjana Lucic-Baroni on Wednesday.
After a routine first set win, Black and Mirza did have to dig out of a mini-hole in the second set, winning four straight games from 3-1 down en route to their 6-3, 6-4 triumph. Their eighth victory in their past nine matches was also their 30th win as a duo.
Joining Black and Mirza in the quarterfinals were No.4 seeds and former Wimbledon champions Kveta Peschke and Katarina Srebotnik, who down a break at 2-1 in the first set against Vera Dushevina and Zheng Saisai won five straight games and went on to a 6-2, 6-3 win.
"The conditions were not easy because it was a very windy day," Srebotnik said. "But we dealt with it really well and I'm really happy about that. We executed well on important points. It's nice to get a win under our belts, especially after having a bye in the first round. It was really important to have a good start, and we did."
Sixth on the Road To Singapore leaderboard, Peschke and Srebotnik's season has been highlighted by a runner-up showing in Doha and a semifinal appearance at the Australian Open.
No.2 seeds and 2012 Rome champions Sara Errani and Roberta Vinci play their opener on Thursday against Darija Jurak and Megan Moulton-Levy. The Italians' 2014 clay court season has been perfect so far, with titles in Stuttgart and Madrid.