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.
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