During the second minute of West Brom's 3-0 defeat at the Etihad Stadium on Saturday, Wilfried Bony was fouled outside the box by Dawson, with referee Neil Swarbrick allowing play to go on before McAuley dispossessed the Ivorian.
Swarbrick then awarded a free-kick for the initial infringement, but inexplicably sent McAuley from the field - despite Dawson appearing to concede that he should be the one to go.
On Monday, the Football Association upheld West Brom's appeal for a case of mistaken identity and the one-match ban has subsequently been transferred to Dawson.
Dawson will now miss West Brom's home Premier League meeting with QPR on April 4 after the international break.
It is the second case of mistaken identity this season in the Premier League after Wes Brown was sent off during Sunderland's 2-0 defeat at Manchester United last month.
The defender was adjudged by referee Roger East to have brought down Radamel Falcao inside the penalty area.
Replays showed that John O'Shea was the man to have committed the foul yet, although O'Shea protested on behalf of his team-mate, East dismissed Brown.
In that case, Brown's suspension was withdrawn and no punishment was transferred to O'Shea.
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