Jose Mourinho's men were headed for a repeat of their 1-0 defeat at Old Trafford two weeks ago when Cristiano Ronaldo scored a magnificent 65th-minute volley, but a late turnaround was made possible when Juan Mata curled in a free-kick four minutes from time.
Pogba then wheeled away in celebration after Alex Sandro put the ball into his own net under pressure from the France international with less than a minute left on the clock, but the World Cup-winning midfielder admitted he had mixed emotions.
"I celebrated, but it was strange," he told BT Sport. "It might have touched a lot of people.
"Lovely, we won. I saw the [Juve] fans, they were very welcoming. I appreciate that.
"We played against a good team with very good players, but the most important thing is the three points.
"I think it's what we’ve been doing for the last few weeks, playing well together and doing well until the end.
"The game is always 90 minutes, we’re pushing, maybe have an extra bit of power at the end, we push it and score."
Pogba, who spent four years with the Bianconeri after leaving Manchester United in 2012, could be seen applauding the home fans after the full-time whistle.
The shock victory has seen United regain second place in Group H from Valencia, with the Red Devils now just two points behind leaders Juventus.
Jose Mourinho’s side will play Young Boys and Valencia in their final two group matches, with qualification now firmly in their hands.
United have now won more away matches at Juventus than any other side in the competition, having beaten the Bianconeri on three separate occasions in Turin.
The first of those wins came during the semi-final stage in 1999, when a late winner from Andy Cole saw the Red Devils see off Juve and qualify for the final in dramatic fashion.
The two sides met again during the group stages in 2003, with a brace from Ryan Giggs and a strike from Ruud Van Nistelrooy helping United on their way to a 3-0 victory.