The clash started after the ball flew out of play and was caught by Moyes, standing in the manager's technical area.
As the Scotsman appeared to be looking to throw the ball to a City player, Mancini stormed into the Everton touchline area and wrestled the ball from his grasp violently and engaged in a war of words.
The incident continued and left referee Peter Walton with no choice but to send the pair down the tunnel although it was the City manager, whose position will come under increasing scrutiny after this setback, who appeared largely to blame.