McAuley was incorrectly dismissed by referee Neil Swarbrick in Saturday’s 3-0 defeat after Dawson fouled Wilfried Bony in the second minute at the Etihad Stadium.
Swarbrick admitted his mistake in a statement from the Professional Game Match Officials Ltd, the organisation responsible for refereeing appointments.
And the FA have confirmed that Dawson will now serve the resulting one-match ban.
A statement on the FA website read: “Following an Independent Regulatory Commission hearing, a claim of mistaken identity in relation to West Bromwich Albion???s Gareth McAuley was successful.
“The player was dismissed during the game against Manchester City on Saturday for denying an obvious goal scoring opportunity.
“The standard punishment of a one-match suspension has been transferred to Craig Dawson and will be served with immediate effect.”
West Brom manager Tony Pulis called for the use of video technology in the Premier League following the incident.
It is the second such controversy in the top-flight in three weeks and the third in a year after incidents involving Sunderland and Arsenal.
“Refereeing is not easy, especially at the level we are at now and how quick the game is,??? said Pulis, who suggested managers get two challenges in a game.
“This product is one of the greatest products this country now sells all over the world, but it is no good moaning about referees. What we have to do is find a way to help referees.”