The Frenchman claimed two assists and ran the show from deep as United - after three successive festive stalemates - won for the third game in a row to move 12 points behind the leaders, who saw their unbeaten record ended at Anfield on Sunday.
Jose went into the game looking for a first win over the Staffordshire side since he took charge of the Reds, having picked up three consecutive draws in his 18 months at the helm. This time around, though, the result never looked in doubt from the moment Antonio Valencia put United ahead inside ten minutes.
Stoke, who sacked manager Mark Hughes last week, were under the caretaker stewardship of coach Eddie Niedzwiecki for their trip to Old Trafford with new boss Paul Lambert, who was watching from the stands, to take full-time charge having been named as Sparky's successor in a bid to maintain Premier League status.
United started strongly and had a penalty appeal waved away early on when Anthony Martial went down under a challenge from Stoke debutant Moritz Bauer. Nothing was given, but the Reds stayed on the front foot and took the lead on nine minutes with the next attack. Pogba picked out Valencia and the returning Ecuadorian marked his comeback in style when he cut inside Josh Tymon and fired home a stunner from 16 yards for his third goal of the season.
Stoke, firmly embroiled in the congested battle for survival, carved out chances of their own. Stephen Ireland - on his first league start since 2015 - fired wastefully wide when well-placed, and Xherdan Shaqiri then tested David de Gea from distance. Following the Potters best spell of the game, Juan Mata and Valencia linked up well but the Spaniard's appeals for a spot-kick were waved away by referee Anthony Taylor.
United moved 2-0 ahead eight before the interval with a goal that was made in France. Pogba surged upfield and cut the ball back for Martial who applied a superb 20-yard finish with aplomb for his tenth of the campaign. Stoke almost halved the deficit in first-half stoppage time when the ball fell to Shaqiri inside the box, but De Gea saved superbly before Peter Crouch's follow up was snuffed out by Chris Smalling.
After half-time, Jack Butland denied Martial and Romelu Lukaku in quick succession, and Mata also went close before the Reds put the result beyond any lingering doubt on 72 minutes.
Top scorer Lukaku added late gloss to the scoreline when he rifled home on the turn for his second goal in as many games. Substitute Marcus Rashford almost the fourth with a nice back-heel, but Butland denied him as the Reds eased to a routine win despite never hitting top gear.
Overall team performance: 7/10
United Faithful Man of the Match: Paul Pogba. A (nother) string pulling masterclass and a joy to watch. Magnificent again.