Timothy Weah headed in the opener after 14 minutes before Buddies goalkeeper Vaclav Hladky saved an Olivier Ntcham penalty.
And the visitors did not seal the points until five minutes from time when Ryan Christie’s strike maintained Celtic’s 13-point lead at the top of the table with just six games remaining.
Rangers at least increased their grip on second place by bouncing back from Sunday’s 2-1 defeat to Celtic with a comprehensive 3-0 victory over Hearts at Ibrox.
Jermain Defoe, deputising for the suspended Alfredo Morelos after his fifth red card of the season at the weekend, opened the scoring and Connor Goldson put Rangers two ahead inside 21 minutes.
Scott Arfield finished off the contest two minutes after the break as Steven Gerrard’s men opened up an eight-point lead over Kilmarnock and Aberdeen.
Kilmarnock were held 0-0 by Hibernian at Easter Road as the Edinburgh side secured their place in the top six for the final five games of the season.
Aberdeen moved level on points with Killie in the battle for third as Niall McGinn scored twice in the final 19 minutes to secure a 3-1 win over Motherwell.
Dundee remain two points behind St. Mirren at the bottom of the table as they lost 2-0 at St Johnstone and Hamilton are also still in the relegation battle after a 2-0 defeat at Livingston.