The fourth-seeded Kops-Jones and Spears were down two breaks at 5-2 in the first set and had to fight off three set points, and also overcame a set point in the second set tie-break before eventually pulling out a 76(2) 76(6) triumph.
"It was a really good match," Spears said. "There was a lot of intensity, and I know all four of us really wanted it. I got lucky on a couple let-cords. They got lucky on a couple lines. We were really happy to get through that.
"The clay is a bit faster here, which suits our game. And there's a little more altitude. I think we're feeling more comfortable on the clay this year than in previous years. We've worked on it a lot."
"We were really bummed that we lost that match in Moscow," Spears said. "But also it's one of my greatest memories because of the atmosphere, being in Russia and playing to get to the WTA Championships. I had never been in that situation. Neither had Raquel. We really enjoyed that and that made us a little bit hungrier this year. Of course, that doesn't always go according to plan, because sometimes when you really want it, you don't play as well. But that's something we're trying to work through and that is our goal - to qualify for Istanbul."
Sure enough, Kops-Jones and Spears were just 5-9 on the season before last week, but have shown their 2012 form in reaching the semifinals in Oeiras and now the quarters in Madrid.
Also securing quarterfinal berths were Cara Black and Marina Erakovic and Kristina Mladenovic and Galina Voskoboeva, who were down 62 42 against Natalie Grandin and Vladimira Uhlirova before rallying for a 26 64 108 victory.
The Top 3 seeded duos are all in action Wednesday, highlighted by top-seeded Andrea Hlavackova and Lucie Hradecka taking on Svetlana Kuznetsova and Flavia Pennetta. Kuznetsova and Pennetta upset the Czechs en route to the semifinals of Miami in March.