With just over half an hour played, Erin Cuthbert fired a distance shot that the referee judged to take on Ellen White's arm.
The referee signaled a penalty for the home side after 26 minutes, amid vocal protests from the visitors.
The replay pictures showed that Manchester City were probably right when they complained about Rebecca Welch's ruling.
White received a yellow card and Chelsea received a penalty which Maren Mjelde pushed in to 1-0.
Chelsea is undefeated
The reigning champion made it 2-0 through Sam Kerr in the 57th minute before Chloe Kelly reduced the penalty.
Then Chelsea responded quickly through Fran Kirby who overall made an impressive effort on his right wing.
The loss was Man City's first of the season. Chelsea is still undefeated, but still only third in the table.