Pep Guardiola's side appeared on course to be crowned champions with a record six games to spare when they eased into a 2-0 half-time lead.
Vincent Kompany's powerful header broke the deadlock before Ilkay Gundogan spun away from Nemanja Matic to double the home side's lead five minutes later.
Yet City crucially failed to land the knockout blow, allowing United to climb off the canvas after the break and make sure their rivals have to wait to secure the trophy for a third time in the Premier League era.
At the end of a week where Guardiola had revealed to the media Pogba was offered to City in the January transfer window, the Frenchman scored twice in the space of two minutes to draw his team level.
Chris Smalling volleyed home the winner in the 69th minute, handing City a second straight defeat following their 3-0 Champions League reverse at Liverpool on Wednesday. Raheem Sterling hit the post and David De Gea saved superbly from Sergio Aguero in a frantic last five minutes, but United just about held on.
City's form throughout the campaign had made it less of a title race and more like a procession. However, despite having the finishing line in sight, Guardiola had to also look ahead to the return leg with Liverpool.
With that game in mind, the Spaniard decided to keep Kevin De Bruyne in reserve, the Belgian among a powerful bench that also included the fit-again Aguero.
United made the short trip hoping to delay the inevitable, and for 25 minutes they stifled their hosts. Yet a City side who have rarely required much help this season were assisted by errors for both of their first-half goals.
Antonio Valencia's miscued clearance gave away the corner that Kompany emphatically headed in, the defender out-muscling Smalling to thump home a finish reminiscent of his derby goal at the same ground six years ago.
The usually reliable De Gea triggered City's second with a weak clearance, Gundogan's pirouette allowing him to toe-poke the ball into the left corner of the Spaniard's net.
A shell-shocked United were fortunate not to be even further behind at the break, with Sterling twice blazing over, before Jose Mourinho's half-time words sparked his side into the most unlikely of comebacks.
Pogba scored twice in the space of three minutes to stun the City crowd, the first a brave finish beyond the advancing Ederson after Ander Herrera had chested the ball into his team-mate's path.
Alexis Sanchez provided the assist for the equaliser, dropping deep to float over a pass his midfield team-mate met ahead of Nicolas Otamendi to head home.
City struggled to recover from the quick one-two, allowing Smalling to provide the knockout blow with a side-footed volley. The defender made amends for losing Kompany for the opener, running in at the back post to convert Sanchez's deep free-kick from the left.
3 - This is the first time that a side managed by Pep Guardiola has conceded 3+ goals in two consecutive matches. Shellshocked. pic.twitter.com/h3wyLZO0ig— OptaJoe (@OptaJoe) April 7, 2018
Guardiola summoned Aguero and De Bruyne in the hope of at least avoiding a second league defeat in the campaign, and the former was denied a 200th goal for the club when De Gea acrobatically tipped over a close-range header.
Sterling hit the post from the resulting corner, but City failed to find a leveller. While the result does not change the title race, with the gap still at 13 points, United at least silenced their noisy neighbours for the time being.
Key Opta stats:
- Manchester City lost a Premier League game they were winning by a two-goal margin for the first time since October 2008 vs Liverpool.
- Manchester United have won nine Premier League away games when trailing by at least two goals – four more than any other side in the competition.
- This was the first time a side managed by Pep Guardiola has conceded at least three goals in consecutive games in all competitions.
- Both Chris Smalling and Paul Pogba have won all nine Premier League games in which they've scored; only Ryan Babel has a better 100% record in the competition (11/11).
- There were just 97 seconds between Pogba's first and second goals.