Stevie MacLean cancelled out Kris Doolan's early opener in a bright first half, but the Saints striker missed a golden chance in the final minute as both sides missed the chance to vault into the top six.
Thistle were rewarded for an enterprising start with a goal after just six minutes when Doolan took advantage of Steven Anderson's slip to get on the end of Aaron Taylor-Fletcher's through-ball before rounding Alan Mannus and rolling home from a tight angle.
Stevie May tested visiting keeper Paul Gallagher with a rasping 20-yard drive, but Thistle almost doubled their lead when Doolan glanced wide from from another Taylor-Fletcher cross.
Gallacher then reacted smartly to beat away a deflected free-kick from David Mackay, and Mannus also produced an excellent save to keep out a fierce Callum Higginbotham drive.
Mannus dealt with another header from Doolan before Saints drew level three minutes from the break as MacLean found the bottom corner with a crisp left-foot shot from Patrick Cregg's neat lay-off.
The home side looked brighter after the break and Chris Millar's well-struck effort from the edge of the box was tipped wide of the post at full stretch by Gallacher.
The Thistle goalkeeper made a near-identical save from May, and the introduction of James Craigen almost produced a second goal for the visitors, but his fine set-up work was undone by Doolan's wayward shot.
But Saints should have snatched all three points in the final minute when MacLean darted behind the defence and cut back for an unmarked Mackay, who scuffed his shot straight at Gallacher.