Having seen 11th-place Motherwell thrash Hamilton Academical 4-0 on Friday, a win at McDiarmid Park became all the more pressing for Gary Teale's men.
However, Brian Graham opened the scoring shortly after the half-hour mark with Steven Anderson's second-half header sealing the points as the hosts returned fifth.
Ross County's 2-1 win against Kilmarnock puts them seven points clear of St Mirren with Michael Gardyne and Craig Curran on target before the hour - Lee Ashcroft netting a consolation for the visitors.
Ronny Deila's men had not played in the league since the loss to St Johnstone on March 4, but first-half goals from Gary Mackay-Steven, John Guidetti and Jason Denayer took Celtic five points clear at the top.
Their closest challengers Aberdeen were held 1-1 at Dundee - Stephen McGinn cancelling out Adam Rooney's opener - while Partick Thistle left it late to beat Inverness Caledonian Thistle.
Steven Lawless tucked home the only goal as Partick won back-to-back league games for the first time since promotion to the Premiership.
