Frenchman Pogba teed up compatriot Anthony Martial for the equaliser before tapping in a third, helping Jose Mourinho's side overcome Dwight Gayle's 14th-minute opener to stretch their unbeaten run at home to 38 games.
Chris Smalling had nodded the hosts ahead in first-half stoppage time while Romelu Lukaku ended his personal drought after the break, the Belgian striker smashing in his first club goal since September 30.
Mourinho allowed Ibrahimovic a late cameo off the bench, the Swede making his first appearance in 216 days since suffering a serious knee injury in April.
The result sees United reclaim second place from Chelsea and remain on the coat-tails of pacesetters Manchester City, who won 2-0 at Leicester City earlier on Saturday to lead their neighbours by eight points.
With Eric Bailly and Phil Jones both ruled out through injury, Victor Lindelof was handed a starting spot in a team that reverted to a flat back four after lining up with three centre-backs in the defeat at Chelsea on November 5.
The defender barely put a foot wrong in helping Sweden stun Italy in the World Cup play-offs, yet one unfortunate slip let Newcastle in to take a shock lead.
Lindelof looked in position to cut out DeAndre Yedlin's cross until he lost his footing, allowing the late-arriving Gayle to stride onto the ball and angle a low shot across De Gea and into the net via the goalkeeper's right post.
United were fortunate Jacob Murphy narrowly failed to repeat the trick soon after before they turned the game around with two headers before the break.
Both were laid on a plate by sumptuous crosses, starting with Pogba cleverly creating space on the right to set up Martial's equaliser with a clever clip to the back post that allowed his fellow Frenchman to beat Yedlin in the air.
Ashley Young followed his team-mate's lead to create the second, as his lofted ball from the left allowed Smalling - who had stayed forward after United had opted to work a short corner - to nod the hosts ahead.
The half-time scoreline was harsh on Newcastle, who had defended doggedly and carried a threat on the counter. However, any hopes they had of picking up something on their travels disappeared when United extended their lead nine minutes into the second half.
Once again Mourinho's side profited from a pinpoint cross, Lukaku's ball in from the right appearing to tee up Marcus Rashford. However, rather than go for goal, the England international unselfishly cushioned a header inside to allow the advancing Pogba to mark his comeback from a hamstring problem with the easiest of finishes from inside the six-yard box.
Lukaku put two first-half misses to the back of his mind to round out the scoring, exchanging passes with Juan Mata before lashing a shot beyond Rob Elliot as United inflicted Newcastle's heaviest defeat under Rafael Benitez.
The loudest cheer of the night, however, was reserved for Ibrahimovic's introduction in the 77th minute. His every touch was hailed by the crowd and he so nearly marked the occasion with a goal, Elliot keeping out an acrobatic volley that demonstrated how the Swede has lost none of his flair for the dramatic during his lengthy absence.
