Forward Lindsey Thomas continued her fine recent run of individual form to steer the Giallorosse into a 2-0 lead inside the first hour - but Betty Bavagnoli's side somehow saw that advantage squandered as the Rossonere emerged victorious thanks to three late goals.
There was a huge element of fortune attached to the Milan goals - new signing Berglind Bjorg Thorvaldsdottir appeared to handle the ball prior to her deflected opener, while Refiloe Jane equalised with a hopeful-looking cross that looped into the far corner - as they got back into the game.
With Roma panicking, in the closing minutes Thorvaldsdottir added her second of the game to complete the turnaround.
Instead of building an advantage in the race for second in Serie A, Roma now sit just a point ahead of Milan - having played a game more. They host Fiorentina next week, in another huge clash at the top of the table.
"We're really disappointed," Bernauer said.
"We were dominating the game and then something changed. We need to work hard to avoid this happening again. We want to win against Fiorentina."
The result will be especially disappointing given the way Roma had impressed for large parts of the match, with Thomas - who now has eight goals this season - providing the decisive finishing touches to give the visitors a lead they appeared to be good value for.
Her first goal may have been somewhat fortuituous - the Milan goalkeeper missing Andressa Alves' deep free-kick, giving Thomas a simple tap-in - but her second was evidence of her growing confidence; as she rifled a low drive into the bottom corner from 20 yards out.
At that point Roma seemed to be flying; alas Thorvaldsdottir's fortunate strike would instead open the door for Milan to produce a remarkable comeback.
"The goals we conceded aren't down to bad luck," Bavagnoli said.
"In the second half we showed the character required to push on, attack and score again - but then we started to back off and I had to make changes. We played well, we had the chance to bring home and we're very disappointed with that - but we'll try again."
See more photos from the game in the gallery below.
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