Hibs trailed Celtic 1-0 at half-time, but the home side hit back through a 27-minute Abi Harrison hat-trick.
Stirling University held Glasgow for 54 minutes before Hayley Lauder, Sarah Crilly and two from Haley Rosen sealed the visitors' victory.
Elsewhere, Glasgow Girls beat Jeanfield Swifts 5-3.
Hearts Ladies against Hutchison Vale was postponed, with a date still to be re-arranged for the tie.
The semi-final draw will take place at Hampden Park on Monday.

The charges were laid in 2014 after a number of women complained to Toronto police that Mr Ghomeshi had been physically violent towards them.
He denies all the charges, saying his actions were consensual rough sex.
If convicted, the 48-year-old - who was sacked by Canadian Broadcasting Corporation (CBC) in 2014 - could be sent to prison for life.
At CBC he hosted the popular arts show Q.
A crowd of reporters and onlookers met Mr Ghomeshi as he arrived at court in Toronto on Monday.
He faces four counts of sexual assault and one count of choking.
A number of women earlier accused him of punching, strangling and battering, and three of the alleged victims later became plaintiffs in the case.
Throughout the investigation, he denied the allegations and later pleaded not guilty to all the charges.
The CBC began an inquiry into Mr Ghomeshi's sexual activities after Canada's Toronto Star newspaper began investigating allegations by an ex-girlfriend that he had engaged in non-consensual, violent sex with her.
After being shown "graphic evidence" that Mr Ghomeshi had physically injured a woman, the broadcaster fired him in 2014.
Holders Glasgow City and last year's runner's up Hibernian have both made it through to the semi-finals of the Scottish Cup.
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Canada's former popular radio host Jian Ghomeshi has gone on trial on charges of sexual assault and choking.