Venus's victory is projected to put her in line for a place in the United States Olympic team, a remarkable achievement in her comeback after she was diagnosed with Sjogren's Disease, which saps her energy, during last year's US Open.
"Seriously," she said, before doing a fist pump at her news conference. "I wouldn't have come back so soon but I needed the points to get in the Olympics.
"I probably wouldn't have come back before Wimbledon or maybe even after it. I need to win more but that's great."
Venus will now play
The Russian world number two was pushed hard by her Serbian opponent, with Sharapova saving six set points in the opening set.
But ultimately Ivanovic's wayward serving and inability to close out key points cost her: both players earned eight break points, but Ivanovic converted just two of them compared to Sharapova's four.
The Wimbledon champion began the match impressively enough, forcing three break points and taking two of them in the first set to waltz into the lead.
Cirstea, the world number 45, upped her game in the second set despite her serve continuing to let her down. Though she only landed 38 per cent of her first serves in play, she was not broken and got the better of her Czech opponent late in the set to level the contest.
Kvitova rediscovered her form just in time, powering through the decider to set up a clash in the quarter-finals with
The 12th seed overwhelmed Goerges in a 70-minute contest, breaking her six times en route to a comfortable victory.
Cibulkova will play reigning French Open champion