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.
A strong first-half display from Celtic saw the champions get back to winning ways in the Premiership against Dundee United.
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.
