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.
Holders Glasgow City and last year's runner's up Hibernian have both made it through to the semi-finals of the Scottish Cup.