Alex Oxlade-Chamberlain blatantly handled in the penalty area in the 15th minute, making a diving save to tip away Eden Hazard's shot when Arsenal was already 2-0 down. But Oxlade-Chamberlain escaped any sanction and referee Andre Marriner instead sent off defender Kieran Gibbs for no obvious reason.
Oxlade-Chamberlain was seen saying "it was me" to Marriner but the referee ignored protests, while his assistants also failed to spot the mistake.
Marriner later admitted he made a mistake via a statement from the Premier League referees' body, with officials prevented from speaking publicly to the media.
"Andre is an experienced referee and is obviously disappointed that an error of mistaken identity was made in this case," Professional Game Match Officials said in a statement. "Incidents of mistaken identity are very rare and are often the result of a number of different technical factors.
"Whilst this was a difficult decision Andre is disappointed that he failed to identify the correct player. He expressed his disappointment to Arsenal when he was made aware of the issue."
Hazard scored from the resulting penalty spot and three more goals followed for the hosts as Arsenal was consigned to one of its heaviest losses in manager Arsene Wenger's 1,000th match in charge.
Technology is only used in the Premier League to rule on disputed goals, but Chelsea manager Jose Mourinho called for referees to be allowed to base decisions on video replays.
"The sending off is a big ammunition for people like me that thinks that one little screen in front of the fourth official is a big help against these kinds of mistakes," Mourinho said.
European football's governing body quickly used the incident by Marriner to argue that the Premier League should adopt its five-official system. An extra official is placed behind each goal in Champions League and Europa League matches after UEFA President Michel Platini rejected the use of technology.
"With an additional assistant referee on the end line, referee would not have got that sending off wrong. Technology is not the answer," Platini's head of media, Pedro Pinto, wrote on Twitter. "More eye balls are the answer ... GLT (goal-line technology) helps with goal line decisions, but 5 officials system gives referee more angles of vision. It's not one vs the other."