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 UEFA Champions League reverse at Liverpool on Thursday (AEST). 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.
