The Dunfermline winger made the most of a Christie Elliott blunder to slot home the only goal of a forgettable contest under the lights at East End Park.
The Fifers could have made the win more comprehensive but Connolly somehow contrived to strike the post from point-blank range in the dying embers.
Alan Archibald’s side have now lost all four of their away matches in the league this term. If they are to secure an immediate return to the top-flight, they must find a way to replicate their fine form at Firhill away from home.
The ball was the first victim of a combative opening, a fiercely contested 50/50 between Louis Longridge and Stuart Bannigan resulting in a burst Mitre. Once a replacement was sourced, neither side appeared capable of doing anything creative with it.
A Faissal El Bakhtaoui shot that skewed comfortably wide was Dunfermline’s only effort of a tepid first half.
Partick were far from potent in the final third, but were presented with a glorious chance to claim the lead when a sloppy pass by Lee Ashcroft inadvertently sent Blair Spittal through on goal, only for the diminutive midfielder to skew wide.
Despite Dunfermline emerging after the break with renewed impetus, Partick almost claimed the lead with a slick counter-attack. Spittal found Kris Doolan at the angle of the box and his powerful drive forced a sharp save from Lee Robinson. This was an underwhelming contest that always looked likely to be settled by a moment of magic or a glaring error.
The latter prevailed when Christie Elliot inexplicably sought to control a deep James Craigen delivery, only to knock the ball perfectly into the path of a grateful Connolly who rolled the ball into the net from close range. A welcome gift for Pars boss Allan Johnston.
Seemingly freed by their opener, Dunfermline started to find some fluidity and their sibling duo Jackson and Louis Longridge both came close to doubling their advantage.
However, it was match-winner Connolly who passed up the best opportunity to put the game to bed when he latched on to a low cross from Louis Longridge and somehow contrived to hit the post from six yards when it appeared easier to score.
They almost paid the price in stoppage time, but Lee Robinson produced a fine point-blank save to deny Andrea Mbuyi-Mutombo before Jai Quitongo saw an effort scrambled off the line.