In what was the first Black Country derby in front of fans in 12 years, violence erupted in the stands after Matheus Cunha doubled the visitors' lead in the 78th minute.
Supporters could be seen fighting each other, while a section of fans invaded the pitch.
Police and stewards desperately looked to get the situation under control, with referee Thomas Bramall calling a halt to proceedings in the 83rd minute.
Both sets of players then headed down the tunnel, with Baggies defender Kyle Bartley seen with his child in his hands.
The game eventually restarted following a lengthy break, with Bartley substituted following the incident.
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Commenting on the ugly scenes on talkSPORT commentary, Nigel Adderley said: "There's some crowd trouble away to our left hand side now, there are fans spilling onto the running track.
"There seems to be something going on here, there are players from both sides heading over to the corner to see what's going on.
"The stewards and the police are piling into this area and at the moment things have got very ugly, very quickly here.
"The stewards are tying to user the players away from the scene, there are fans all over the pitch around the corner flag and things have suddenly boiled over.
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"Whether it's Wolves fans in this area of the stand I'm not too sure, but there was a good deal of acrimony, punches have been thrown, the stewards and police are trying to keep supporters apart on the running track but there are fans all over the pitch.
"This is something we did not want to see here today, the security presence has been very strong and now there is a police cordon on the field of play.
"There is supporter carrying a young child in tears away from the scenes they are now on the field of play. There is absolute chaos here."
Former West Ham striker Dean Ashton remarked: "They've completely lost it, some of these supporters. Completely lost their heads!
"Yes I'm sure it is to do with possible Wolves fans in the West Brom end, we see just one man on his own in there being protected almost by the stewards as bests they can.
"You've also got supporters down there who have come from other stands and run along to get involved, and they're throwing things into their own supporters, trying to hit the one guy they're targeting.
"They're separating fighting fans in the stand, they're trying to get that one person out somehow through the melee while people are still throwing things at him.
"He's in a headlock being held back by a couple of stewards. People are just trying to throw punches at that one guy who they're trying to get out of the ground.
"The police are desperately trying to get him out, but the fans just won let them, they're swinging punches at him.
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"A flair and has let off and now the corner flag has been picked up by somebody and thrown onto the field of play.
"This is absolutely disgraceful, what a shameful image for English football."