Everton and West Ham on Thursday both won challenges against dismissals, with the Toffees seeing Darron Gibson's punishment wiped out.
Cole was sent off by referee Anthony Taylor in the 67th minute for a high tackle on Leighton Baines which was determined to be dangerous.
It came soon after his opening goal was matched by an equaliser from Victor Anichebe, and Everton went on to take all three points thanks to a Steven Pienaar goal six minutes later.
West Ham succeeded with their case at a Football Association hearing, meaning Cole will be available for Saturday's Premier League match against Reading.
Cole wrote on Twitter: "Great news that the red card got overturned, @FA done a great job. Well done! Time to make all the aggro worth it on Saturday if selected!"
While Cole was ordered off midway through the second half, Everton midfielder Gibson followed in stoppage time for a similar tackle on Mark Noble during Everton's 2-1 win.
Everton lodged their appeal with the FA on Christmas Eve, meaning Gibson was able to face Wigan on Boxing Day, and he will now be available to manager David Moyes for Sunday's game against Chelsea and beyond.
A statement from the FA said: "The FA can confirm that red cards shown to both Carlton Cole and Darron Gibson have been rescinded.
"Both players were sent from the field of play in the Premier League fixture between West Ham United and Everton at Upton Park on Saturday 22 December.
"Their three-match suspensions have been withdrawn immediately and written reasons will be provided at a later date."