Full-back Gary Sawyer was the hero for the Pilgrims after heading home from eight yards with just four minutes remaining.
The single goal win was Argyle's first victory in five games and only their third win in 17 to halt a depressing slide down the table.
For Tony Parkes' side, the defeat ended a four-game unbeaten run and left them still with plenty of work to avoid a relatively swift return to League One.
Leading scorer Paul Gallagher had the visitors first chance in a dire first half but saw his long-range effort dip just over the bar.
Loan signing Lee Hughes, captured for the remainder of the season from Oldham Athletic, was the chief threat for the home side in the opening stages with a long-range effort and header which keeper Romain Larrieu was equal to.
Then just as the half came to a close, Pool keeper Paul Rachubka did well to smother a sharp effort from Jamie Mackie.
Despite the early loss of joint leading scorer Dudley Campbell early in the second half, the home side gained the upper hand but had two goals disallowed.
Firstly, on loan Glasgow Rangers midfielder Charlie Adam finished sweetly but was penalised for a handball before Brett Ormerod also had a goal scrubbed out for an earlier offside.
Seasiders sub Stephen McPhee almost broke the deadlock midway through the second half but couldn't direct his header goalwards after a wicked cross from Adam bounced up just in front of him.
Paul Sturrock's men however forced their way back into the game and had a glorious chance to break the deadlock but Karl Duguid managed to head over from eight yards.
In truth neither side deserved to win a tense scrappy affair but, as the game looked to be drifting into stalemate, up popped Sawyer with his second goal of the season to send the 800 visiting fans into raptures.