Pedro Neto scored in the first half before Matheus Cunha netted with 13 minutes remaining, but tensions boiled over in one corner of the ground, it being claimed on the live television broadcast that a number of Wolves fans had celebrated the second goal while in the home section of the stadium.
As police clashed with fans and several supporters made their way onto the pitch, a 38-minute break was required to restore order, there being no certainty that the game would resume.
When it did, Wolves were able to successfully negotiate the remainder of the contest to advance through to the last 16 without further alarm.
Amid the boisterous atmosphere between two sets of supporters who had not witnessed their respective sides square off in front of a crowd since 2012, goalmouth activity was few and far between during the early stages.
West Brom posed the greater threat, with goalkeeper Jose Sa having to make two routine saves, and they did an effective job on nullifying opportunities for their Premier League opponents.
However, shortly before the break, Wolves were able to take the lead, Matt Doherty leading a break-away from a poor West Brom corner to set Neto on his way.
The Portuguese stormed down the right before drifting inside, being halt knocked out of his stride by an Albion defender, but he impressively kept his balance to send a low shot into the bottom corner from 20 yards out.
Like in the first half, West Brom were the dominant team when play got back underway, Wolves having to withstand a barrage of pressure that sometimes was a result of their own poor decision-making.
As the game entered the final quarter, Wolves had warmed back into the contest, Jean-Ricner Bellegarde sending their only other shot of note in the game marginally wide of the far post from the edge of the area.
Moments later, West Brom should have perhaps equalised, a flowing move concluding with Brandon Thomas-Asante blazing a shot from 14 yards high into the stand.
John Swift then sent a much better-executed effort marginally over from 20 yards, and it proved costly as Wolves added a second through Cunha.
A long ball over the top caught out the Baggies defence and having held off the attention of a defender and kept his composure, the Brazilian slotted the ball through Josh Griffiths's legs and inside the near post from an acute angle.
That goal sparked extremely unsavoury scenes in the stands, a number of Wolves fans seemingly celebrating in the away end and seeing tensions boil over with stewards and police struggling to restore order.
A delay of over half-an-hour ensued, there being doubts over whether the game would be completed and how the issue would be resolved, seven minutes plus at least six minutes of added-on time remaining.
Play eventually restarted, the referee starting the game from the moment that Wolves scored their second goal, which was 77 minutes 10 seconds, and there was a subdued atmosphere as the players attempted to get back up to speed.
West Brom got back into their stride with Wolves prepared to sit deep and play on the break, and Sa had to be alert to keep out a low effort from Swift.
Down the other end, Griffiths pulled off an outstanding save to deny Cunha a match-clinching third, but after just two minutes of added-on time were indicated, the game reached the quiet conclusion that it required.