Patrick Cregg was also on the scoresheet with a goal against his former employers, on a night when Steven MacLean failed to convert from the penalty spot to boost the scoreline further.
Leigh Griffiths did manage to pull a goal back for the home side late on but his effort failed to spark a comeback.
The game sparked into life when Saints took the lead after 22 minutes. MacLean saw his point-blank effort blocked by goalkeeper Ben Williams before Vine pounced to rifle home the rebound from eight yards.
Vine grabbed his second of the night just four minutes later when he cut inside from the left and sent a superb swerving right-foot shot beyond the grasp of the Hibs goalkeeper.
The Perth club had the chance to add to their tally further when referee Kevin Clancy pointed to the spot on 33 after Ryan McGivern had felled Mehdi Abeid in the box.
Despite Vine chasing a hat-trick, it was MacLean who stepped up for the spot-kick and he was denied a goal of his own when Williams dived to his left to block with what was his fifth penalty save of the season.
Saints still looked dangerous and Abeid was not too far away when he dragged his shot across the face of goal and inches past the upright.
The first half had been frustrating for Hibs and boss Pat Fenlon made a double switch five minutes after the restart, with Paul Cairney and Jorge Claros thrown into the action for Gary Deegan and Alan Maybury.
But it was the visitors who had the net bulging again after 59 minutes.
An impressive passing move culminated with Murray Davidson teeing up the shot for Cregg on the six-yard line and he supplied a composed finish with only the goalkeeper to beat.
There was to be no match ball for Vine when he made way for Nigel Hasselbaink with 20 minutes to go.
Griffiths netted for the home side after 81 minutes when he latched onto a long ball through the middle and lashed past Alan Mannus but the strike proved to be too little, too late for Hibs.
Hasselbaink then had the ball in the net in injury time but a free-kick had already been awarded to the home side.