Arsene Wenger's side looked set to escape a disappointing clash at The Hawthorns with all three points after Alexis Sanchez's free-kick deflected in off James McClean with only seven minutes left.
However, Calum Chambers was penalised for blocking a Kieran Gibbs cross with his hand, allowing Jay Rodriguez to snatch an equaliser from the penalty spot in the 89th minute.
The incident came just 24 hours after Jose Mourinho complained about Craig Pawson's decision not to give Manchester United a spot-kick in their 0-0 draw with Southampton, when Maya Yoshida denied Jesse Lingard a chance at goal by blocking the ball with a raised arm.
Wenger, who was taking charge of a record 811th Premier League game, was spoken to by Dean for his remonstrations on the touchline and confronted the referee in the tunnel after the final whistle.
Cech was also booked after the match after approaching the officials and the 35-year-old was left nonplussed by the decision.
"I got a yellow card for saying that it was not a handball," a visibly furious Cech told Sky Sports. "We have a meeting with the referees at the start of every season, and every time we say that the player is too close to the ball [in such an incident] for it to be a handball.
"So, I asked him why he changed his opinion to give the penalty when every time we have these meetings they say it will not be a penalty. So he booked me and it is most disappointing because he could have told me why. He just walked away and gave me a yellow card."
Asked what Dean said to Cech in reply, the keeper said: "Nothing. I expect when I walk to the referee with respect and ask a question that he answers me in a normal way."