Referee Neil Swarbrick admitted he sent off the wrong man at Etihad Stadium after Dawson had fouled City striker Wilfried Bony in the second minute.
The FA's Independent Regulatory Commission met on Monday and ruled it was a case of "mistaken identity".
Dawson will now serve a one-match ban.
The defender will miss the Premier League visit of QPR on 4 April for denying an obvious goalscoring opportunity.
Northern Ireland centre-back McAuley was dismissed in the second minute for a foul on Bony when it was Dawson who had committed the offence.
Swarbrick apologised for his mistake afterwards via a statement from the Professional Game Match Officials Ltd.
After the game West Brom boss Tony Pulis called for referee reviews, where managers are able to appeal against decisions during a game.
"If we can help referees with a 30-second call-back option, twice a game, it would stop us talking about them," the West Brom manager said.