The Easter Road outfit had fallen behind to Stevie May's 17th-minute opener but Paul Heffernan levelled in the 35th minute before Collins' second-half effort secured a hard-fought victory.
Hibernian, who won 2-1 at Kilmarnock in their last match on their travels, move up into the top six in the Scottish Premiership as a result of their success on Saturday.
Alan Mannus returned in goal for St Johnstone at the expense of Stevie Banks, while Paddy Cregg and May started after missing the goalless draw at Aberdeen a fortnight ago with Gary McDonald and Chris Millar dropping to the bench.
Heffernan was handed a first start up front for Hibs alongside Collins with Rowan Vine dropping to the bench, while Alan Maybury, Kevin Thomson and Scott Robertson came in for injured trio Ryan McGivern, Owain Tudur Jones and Danny Handling.
The hosts started brightly and striker May showed his intent early on as he was sent racing down the left channel by Nigel Hasselbaink only to be thwarted by Maybury as he cut inside.
St Johnstone midfielder David Wotherspoon then lifted a left-foot effort just over from 20 yards as he looked to make an early impression against his former employers.
May already had three goals to his name this term and his pace drew the first caution of the match when he strolled past Michael Nelson only to be hauled back by the visiting centre-half.
The Edinburgh side clearly failed to heed the early warnings from the McDiarmid Park forward and the 20-year-old broke the deadlock 17 minutes in with a terrific strike.
May picked the ball up 25 yards out with his back to goal but spun his marker before sending a ferocious drive beyond Ben Williams and into the bottom corner.
Hibernian responded through Liam Craig with the former St Johnstone favourite forcing Mannus into an acrobatic save midway through the half with a volley from distance after the midfielder's initial free-kick had failed to beat the defensive wall.
However, the Easter Road outfit managed to pull level 10 minutes from half-time.
Collins' turn and shot was deflected into the path of Robertson, whose low drive crashed off the base of the post but striker Heffernan was on hand to roll the ball into the unguarded net for his first Hibernian goal.
St Johnstone started the second half stronger with Murray Davidson firing narrowly over from 18 yards.
A delightful run by May six minutes after the re-start almost led to the hosts restoring their advantage.
The young forward showed terrific strength to hold off Paul Hanlon before he cut inside then back-heeled the ball into the path of Cregg but his first-time strike was blocked by Nelson on the six-yard line.
But it was the away side who edged in front two minutes later.
Craig lifted the ball over the home defence for Collins, who volleyed into the net from a tight angle for his first goal for the club since arriving from Swindon in the summer although Saints goalkeeper Mannus could arguably have done more to keep out the striker's effort.
Mannus partly redeemed himself moments later with a reflex save to keep out Heffernan's 20-yard drive before Hibernian introduced new signing Abdellah Zoubir from the bench for matchwinner Collins with 11 minutes remaining.
The 21-year-old winger had little time to make an impact but Fenlon's men held on comfortably for an impressive away success.