Cup quarter-finalists Partick failed to turn their possession and chances into goals as Peterhead claimed their first win in five games.
The visitors dominated but went behind in the 11th minute. Bobby Linn, who set up both goals, saw his pass deflected into the path of Kevin Nicol who sent a sweetly-struck shot from the edge of the penalty area into the net for his second goal in three games since signing from Hibernian.
Thistle should have levelled after 32 minutes. Jamie Buchan brought down Stephen McConalague, but Marks Roberts, the Thistle hero in midweek, sent his spot-kick well over the cross bar.
The visitors dominated the first half, but Peterhead could have scored again with Linn, Martin Wood and Graeme Sharp all going close.
Partick looked lively from the restart, and after Scott Boyd bulleted a header towards goal in the 53rd minute, they deservedly equalised. Peterhead were left claiming for offside as a pass found Paul Ritchie, but he took one touch before dispatching a low shot into the far corner from the edge of the penalty area.
Peterhead were rarely seen as an attacking force after the break until a Sharp shot was saved by keeper Kenny Arthur which then sparked them into life and they regained the lead after 67 minutes. Linn was the architect again, crossing from the left side of the penalty area for Wood to score from a couple of yards at the back post.
Thistle substitute Sean Kilgannon almost equalised with his first touch, but at the other end Linn was denied the goal he deserved by a fine save from Arthur.