Jonathan Greening's first league goal of the season had set them on the way to victory against a Wolves side who were simply never in contention.
Albion completed their success six minutes from time when John Hartson ended his 13-game goal drought from the penalty spot.
Luckless Wolves substitute Mark Little had only been on the pitch for a few seconds when he hauled down Kamara, allowing Hartson to score his third goal of the campaign with the resulting spot-kick.
The defensive resilience that has been Wolves' hallmark this season was sadly missing and they were also overrun in midfield.
Wolves did at least show more endeavour in the second-half. Jemal Johnson had a shot blocked by Greening, Seyi Olofinjana fired wide and Jay Bothroyd had a low drive saved by Pascal Zuberbuhler.
But by then the damage had been done by a free-scoring Albion side who have now helped themselves to 19 goals in six games since the departure of Bryan Robson.
The margin of their win could have even been greater as Greening saw another drive deflected just over and Matt Murray pulled off a smart save to deny Nigel Quashie.
It was the perfect start for Mowbray following his arrival from Hibernian. The former Celtic centre half has himself admitted that rarely can a new manager have inherited a side in such good form.
In the first meeting between the sides for five years, Wolves, who have now not won at The Hawthorns since 1996, looked strangely subdued when the game began and it was no surprise that Albion needed just 11 minutes to break the deadlock.
Wolves' central defenders Gary Breen and Jody Craddock went missing as Jason Koumas rolled the ball back across the area to Greening who drilled his powerful shot beyond Murray.
Such was Albion's dominance that it looked like only a mistake from them could hand Wolves a way back into the game. They were presented with one after 17 minutes but crucially squandered it.
Zuberbuhler, whose handling was questionable all match, spilled a long-range drive from Bothroyd and the ball ran kindly to Darren Potter.
But the on-loan Liverpool midfield wasted the chance as he fired the ball straight back at the recovering goalkeeper.
It was a crucial miss as Albion effectively sealed their success ten minutes later.
Wolves left-back Jamie Clapham allowed himself to be muscled out of the way by Martin Albrechtsen and the Dane then delivered a telling cross that Kamara headed powerfully past Murray.