For all this pressure all they could muster was a Scott McCulloch shot easily saved by Paul Mathers.
They were punished for this lack of punch on 14 minutes when Peterhead went ahead after their first attack. A long ball was misjudged by Grant Murray and this allowed Martin Wood to combine with Bobby Linn to allow the latter to score from eight yards.
Fifteen minutes later the visitors were two up as Linn piled on more agony for the Jags, this time heading a Jamie Buchan cross into the roof of the net at the near post despite the attention of a handful of Thistle defenders.
Thistle were almost three behind early in the second half but were grateful to keeper Colin Stewart who turned Buchan's shot around the post.
At the other end Thistle finally found a way past Mathers when Billy Gibson's lob cleared the keeper only to find Mark Perry on hand to head clear.
The home side reduced the deficit with three minutes left with a spectacular overhead kick from Graham Dorrans but they were soon two behind as Buchan turned McCulloch to stroke the ball past Stewart in the final minute.