The striker was sent off with just over 10 minutes remaining of the 0-0 draw at Selhurst Park, following a VAR review recommended by Craig Pawson.
In real time, on-field referee Chris Kavanagh did not even blow for a foul, after Calvert-Lewin slid in to keep possession away from Palace full-back Nathaniel Clyne.
As the Everton attack fizzled out, there was a lengthy wait before the restart as the incident was checked, despite no real complaints from any of the Palace players.
After going over to the monitor though, and following multiple replays of the alleged challenge, Kavanagh decided to overturn his decision and give Calvert-Lewin a straight red card.
In the immediate aftermath of the decision, both the referee and the VAR were lambasted over the incident, which has been universally viewed as extremely harsh.
Sean Dyche's men hung on valiantly despite their man disadvantage, even during nine minutes of added time, to force a replay next midweek.
As the challenge was deemed violent conduct, Calvert-Lewin would be set to miss Everton's next three games, against Aston Villa, the replay against Palace, and then either a potential fourth round tie, or their Premier League clash with Fulham.
However, Everton have confirmed that an appeal has been lodged against the decision to the Football Association.
A brief statement from the club read: «Everton Football Club has today notified the FA of its decision to appeal the red card issued to Dominic Calvert-Lewin in our FA Cup third round fixture at Crystal Palace on Thursday evening.»
Dyche has often been calm and composed
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