City climbed over United into third in the WSL standings on 13 points after seven games, six points behind leaders Chelsea, while United have 12 points.
The crowd of 43,615 smashed United's previous attendance record of 30,196 for a WSL game at Old Trafford set in 2022 against Aston Villa.
Captain Katie Zelem put United ahead with a penalty in the 21st minute after Alex Greenwood's handball, but Jill Roord and England international Lauren Hemp scored in the 34th and 35th minutes in a breathless first half.
United gifted City a goal when England keeper Mary Earps hesitated to meet a soft pass back from Maya Le Tissier. Earps' attempted clearance ricocheted off an onrushing Khadija Shaw and into the net, leaving United's keeper angrily yelling about the error.
City were reduced to 10 players in the 72nd minute when Laia Alexandri was shown a second yellow for a foul on Lucia Garcia, and while United dominated with a flurry of chances in the final few minutes, City held strong and their fans were singing "Blue Moon" by the final whistle.
Arsenal beat Brighton & Hove Albion earlier on Sunday for their fifth successive WSL victory with goals from Stina Blackstenius, Caitlin Foord and Frida Maanum. Arsenal climbed back to within three points of leaders Chelsea.
Chelsea, the only undefeated team, had moved six points clear atop the table on Saturday with a 5-1 win over Liverpool that featured a Lauren James hat-trick amid their quest for a fifth successive WSL title.
England international Rachel Daly scored in added time to lift Aston Villa to a thrilling 3-2 victory at West Ham United. Anna Patten and Canadian international Adriana Leon also scored before Daly hooked in the winner from inside the box for Villa, who are ninth with just two wins.
Celin Bezit scored a second-half equaliser to ensure Tottenham left the King Power Stadium with a point in a 1-1 draw against Leicester City. Tottenham are fifth, two spots ahead of Leicester.
Amalie Thestrup scored in the 82nd minute to salvage a 2-2 draw for Bristol City at Everton. Everton are 10th in the table, two spots ahead of bottom side Bristol City.
