Mings and El Ghazi lost their cool in the first half at Villa Park and had to be dragged away by team-mates after West Ham nearly took the lead.
The pair escaped punishment for their row, but Masuaku was not so fortunate as he saw red for a second booking after half-time.
Villa were unable to make their numerical advantage pay off and had to settle for a stalemate that left the spotlight on the bust-up between Mings and El Ghazi.