In an absolute powerfest in the feature night match, Cibulkova and Williams went toe-to-toe under the lights, with Cibulkova coming out far stronger - she went up a set and a break, 61 10 - but Williams fighting back to take the second set, 7-5, though she did have a set point a few games earlier at 5-3.
Things were streaky in the third set - Cibulkova stormed out to a 4-1 lead, then Williams cut that lead down to 4-3 and had points for 4-all. But the last push went the No.10-seeded Cibulkova's way, as she closed the No.29-seeded Williams out with that aforementioned forehand winner, 61 57 63.
Cibulkova, who is currently at a career-high ranking of No.11, is one win away from breaking the Top 10 for the first time - if she wins her quarterfinal match on Wednesday she'll break the elite.
Standing in her way of that honor - and the semifinals - is No.3 seed Radwanska, who battled two hours and 33 minutes earlier in the day to make it past Ukrainian teenager Elina Svitolina, 76(5) 57 62.
"It was really tricky because I didn't know her and she played really solid tennis in all three sets," Radwanska said. "She's a great player and had a really good run here - a couple of very good wins.
"I think she's really playing some very good tennis these days."
After getting broken when serving to stay in the second set at 5-6 - and obviously dropping the set there - Radwanska had an uncharacteristic display of anger with her racquet. But after the match, the always-bubbly fan favorite showed her funny side, an impressive ability to block the incident out.
"That's the first time I'm hearing about that!" she joked when asked about it.
"I don't know what we're talking about, seriously!"
Radwanska leads Cibulkova in their head-to-head series, 5-2, but in their only previous meeting this year, in the semifinals of the Australian Open, Cibulkova ran away with a lopsided 61 62 victory.
"It didn't go my way last time," Radwanska said. "I hope it will be a good match this time."