The Chilean was in the right place at the right time to hand the Old Lady three points in Sicily, but the match will be remembered for two incorrect decisions
Gonzalo Bergessio had poked the home side into the lead, only for an erroneous linesman's flag to cut their celebrations short.
To make matters worse, Nicklas Bendtner was stood in an offside position in the build-up to Juve's winner, while Giovanni Marchese was dismissed for two bookable offences.
Bendtner, who was largely wasteful, headed Kwadwo Asamoah's cross into the ground and straight at Mariano Andujar after 21 minutes, and Marchese produced a dangerous cross after a burst to the byline at the other end as the game opened up following a cagey opening.
Bergessio looked to have given the hosts the lead when he tapped into an open net after Nicolas Spolli's glancing header had come back off the post. But the Sicilians' joy quickly turned to fury when the linesman raised his flag for offside, despite the fact that neither Bergessio, nor any of his team-mates, were even close to being beyond the last defender.
The home side were clearly angered by the decision and Spolli, Pablo Cesar Barrientos and Marchese were duly shown bookings for infringements varying from dissent to cynical fouls.
As the hosts struggled to compose themselves, an offside Bendtner headed Andrea Pirlo's free kick against the crossbar and Pogba sent a dipping effort just inches over the goal to highlight the Bianconeri's dominance.
The Elefante picked up their fifth booking inside the opening 38 minutes when Nicola Legrottaglie was booked for handball, just as Alexis Rolin had been earlier in the afternoon.
Vucinic had a great opportunity to put his side ahead when through on goal from the resulting free kick, but he was denied by the recovering Legrottaglie. And the Montenegrin was denied again just two minutes later when keeper Andujar reacted well to keep out the striker's close-range effort on the line.
Pirlo stung the shot-stopper's palms from 20 yards shortly afterwards, but the game remained goalless at the break.
The only goal of the game arrived in typically controversial circumstances 11 minutes into the new half.
Vucinic picked out Bendtner with a clinical pass from the edge of the area, only for the Danish striker to shoot tamely - and typically - at Andujar. But the impressive Argentine shot-stopper could only push the ball into the path of Vidal, who tapped into the unguarded net.
Replays showed that Bendtner was in an offside position, which did nothing to placate the fired-up home support.
Vidal waltzed through the home defence on 64 minutes but could only drag his shot wide, yet the home side were soon to be dealt a near fatal blow when Marchese was shown his marching orders when he picked up his second yellow card for an amateurish handball.
As ever, Pirlo drifted the resulting free kick into a dangerous area, but Pogba's downward header was well saved by Andujar.
The game lost any impetus following the red card, but Sebastian Giovinco's arrival went some way to adding a new dimension, and the diminutive Italian saw a sweetly-struck effort well saved by Andujar seconds after coming on.
Lichtsteiner almost gifted the home side an equaliser with 10 minutes on the clock when he headed past Gianluigi Buffon, but into the side netting.
Vidal again stung the palms of Andujar with three minutes on the clock, and Giovinco tore through the home defence before blazing over.
It was another significant victory for Antonio Conte's champions, who again showed they have the stomach for a fight as they have done against Chievo and Napoli already this season.
Catania, who have not beaten the Turin side in Serie A since 1964, will be furious that they were robbed of the opportunity to do so here thanks to that shocking offside call.