He is now available for selection for Sunday's Championship game against Barnsley at Ninian Park.
But, more importantly, Purse should now be able to lead the Bluebirds out at Wembley in the FA Cup final - a game he would have missed had the suspension been upheld.
Cole had dubbed Purse a 'muppet' after the incident at Turf Moor, but Cardiff manager Dave Jones defended his player after the game.
"I thought the sending off was harsh. I'm not biased. I speak as a former defender," Jones said.
"It was not intentional. If we are coming down to things like that being a sending-off then every mis-timed tackle or everything we do is going to end up like that."
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