City dominated the first half and led through Chloe Kelly and Laura Coombs. But United came out fighting in the second and levelled thanks to goals from Tobin Heath and substitute Kirsty Hanson.
Here's what United manager Casey Stoney and City boss Gareth Taylor had to say about the events at Leigh Sports Village.
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City's Dominant First Half Performance
"I thought we looked dangerous, played through them in the first half, created numerous chances," Taylor told BT Sport. "We just needed to stick a few more away. But the effort and attitude and some of the football we played in the first half was top class.
"Performance-wise I've been pleased. There's real elements of our game that have been top. Some of the play was really, really good. We just need to provide that on a bit more of a regular basis and create that consistency a bit more."
Manchester United's Improved Second-Half Performance
"I take full responsibility for the first half," Stoney told BT Sport. "I think I got the press wrong so I had to change that at half time to make sure we pressed differently because I think they were picking us off.
"I think the players were incredible in the second half. I think I'm more proud of today - because we were 2-0 down and the mentality shift - we might have folded last year. I think we were unfortunate in the end not to win it."
United's Substitution-Inspired Comeback
"Unbelievable. And that's why we call them [substitutes] game changers," said Stoney. "It's not credit to my substitutions, it's credit to them because they come on and they really apply themselves.
"There's a mindset now, a mentality shift. We can go toe-to-toe and we can beat teams. 2-0 down against Man City is not an easy feat at half time and they've come out and been the far better team.
"That second-half performance was for our fans, to make sure we got that result in the Manchester derby which is really important for them."
City Throwing Away a Two Goal Lead
"Bit disappointed with the second half," Taylor added. "I think we were so in control in the first half, absolutely bossed the game. We could have arguably been two goals better than what we were - we're probably looking at a three or four goal scoreline with the opportunities we created.
"But at half time it was a good situation to be in and looking at implementing our game in the second period which I didn't think we did enough of.
"It's disappointing, it feels like three points dropped, especially in the commanding position we were in."
United's Topping of the Table
"It [being top of the table] doesn't matter," Stoney added. "It's November. Even the first half today showed the last game doesn't matter.
"It's about performing and being at that consistent level week in week out and we know we can't concede those sort of goals and play like we did in the first half and that was enough motivation to make sure we keep going to the next level."