Third-placed Motherwell ended a three-game winless run by edging St Johnstone 2-1 at home.
Stephen McManus headed home the deciding goal before half-time to send Stuart McCall's side six points clear of fourth-placed Dundee United, who could only draw 1-1 at Inverness Caledonian Thistle due to a superb performance from home goalkeeper Dean Brill.
Motherwell only require one point from their final two outings to secure European football.
Champions Celtic ran out 5-2 winners against second-placed Aberdeen, who are now just a point above Motherwell.
Celtic have long since secured a third successive title, but required victory on Saturday to maintain their chances of breaking the 100-point barrier.
Neil Lennon's men ultimately triumphed at a canter, with Scott Brown and Kris Commons each grabbing two goals.
Gregg Wylde's 79th-minute thunderbolt earned St. Mirren a 1-0 win over Ross County, heightening the latter's relegation fears.
County are just a point above Kilmarnock, who visit Hearts on Sunday and currently occupy the relegation play-off place.
Hibernian and Partick Thistle each moved a point above Ross County following an entertaining 1-1 draw.
Kris Doolan's tap-in gave Partick an early lead, but Hibs avoided a seventh successive defeat - despite losing Michael Nelson to a red card - courtesy of Sam Stanton's late header.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.