Kamara scored one goal and made another as Albion repeated the 3-0 league win they enjoyed against Wolves at The Hawthorns in October.
Kamara and Kevin Phillips struck five minutes apart either side of half-time and substitute Zoltan Gera pounced in the 78th minute to sentence Wolves to their heaviest home defeat of the season.
Wolves could have few complaints about the result as they were generally second best to an Albion side who have now won back-to-back away games after going three months without a win on the road.
The setback only served to continue Wolves' poor run at home where they have now won just two of their last nine games.
Manager Mick McCarthy tried to inject some life into his side by sending on striker Stephen Ward and Mark Davies at half-time, but even before they had a chance to settle, Wolves' fate was sealed by Phillips.
In the first FA Cup meeting between the sides since 1962 when Albion won 2-1 at Molineux, Tony Mowbray's side should really have been in front well before Kamara's goal in the 44th minute.
While there was plenty of effort and endeavour about the play of Wolves, Albion looked by far the more threatening side when they went forward.
Senegal international Kamara himself was guilty of missing two golden chances in the opening 20 minutes having his first shot was blocked and then seeing his second whistle just wide.
When Jason Koumas ended his mazy run by also firing inches past the post it seemed only a matter of time before Albion's pressure would pay.
Wolves, who threatened briefly when Seyi Olofinjana saw his 23rd minute shot deflected wide, were finally undone when they committed too many men forward in attack.
Kamara blocked a shot from left-back Jackie McNamara and was then sent clear by Phillips. He used his speed to comfortably out-pace right-back Mark Little before waltzing around goalkeeper Matt Murray to walk the ball into an empty net for his 15th goal of the season.
It was a crucial time to score and Wolves never recovered as they were caught cold at the start of the second half.
This time Kamara turned provider to tee-up Phillips who cut in from the left-hand edge of the area before curling home his 12th goal of the campaign.
To add to the agony for Wolves, Gera then stabbed home a corner from Koumas to give the final scoreline a resounding look.