Seeing Man City win the title would be like death – Pogba
City were 2-0 up at half-time thanks to goals from Vincent Kompany and Ilkay Gundogan, and Pep Guardiola's men appeared to be in complete control.
But United fought back in the second half, with Pogba playing a starring role as he scored twice in quick succession early on.
Chris Smalling then got the winner to stun City, whose hopes of sealing the Premier League title against their bitter rivals were dashed.
And for Pogba, who Guardiola claimed on Friday was offered to City by agent Mino Raiola in January, losing the derby last season was still playing on his mind heading into the clash.
"I didn't want to lose against City," he told Sky Sports. "The loss from last season is still in my mind.
Ladies and gentlemen, your #MUFC Man of the Match on derby day...@PaulPogba pic.twitter.com/TEKLtBWH49
— Manchester United (@ManUtd) April 7, 2018
"If they won they are champions, for all the fans it would be like death. To lose against City and to see them celebrate, I couldn't let that happen.
"At half-time in the dressing room we said we have nothing to lose."
Pogba's two goals both came from late runs into the penalty area from deep and he credited a United stalwart's influence in that.
"Michael Carrick has helped me a lot with these late runs," added the France international. "He always shows me videos of what I should be doing.
"With City, they love to attack, they don't like to defend, so I had to get more in the box. I knew I had Nemanja Matic behind me and Ander Herrera with me.
"For the goal I didn't think about anything. With Alexis Sanchez, he likes to play direct. I saw the space and just went. I was lucky Kompany wasn't tight enough."