The Baggies moved to within one point of second-placed Preston in the Coca-Cola Championship thanks to goals from Jonathan Greening, Diomansy Kamara and John Hartson.
They have now won four successive matches since the end of the Bryan Robson era.
Mowbray said: “I’ve been around the place for a week or so and I know what they are capable of.
“Wolves started a bit brighter in the first five minutes but, for the rest of the first half, we played with a lot of purpose and desire and quality, created chances and got our noses in front.
“We talked at half-time about how to protect the lead and how precarious a 2-0 lead can be in football. We dropped off a bit in the second half and allowed them too much of the ball.
“But we’ve won the game 3-0 and I’m delighted for the players and the fans. Local pride is important, it’s important you win derbies and I am pleased with the outcome.
“All derbies have got their own bit of magic. It is quite a sight when you see the ground bouncing up and down like that at 2-0 and 3-0.
“We have Arsenal in the Carling Cup on Tuesday and another derby at Birmingham on Saturday and it keeps rolling on – but you want to be involved in big games.”
WEST BROM: Zuberbuhler, Albrechtsen, Curtis Davies, Perry, Robinson, Gera (Watson 86), Koumas (Chaplow 74), Quashie, Greening, Ellington (Hartson 66), Kamara.
WOLVES: Murray, Edwards (Little 83), Breen, Craddock, Clapham, Ricketts, Henry, Potter (Craig Davies 72), Olofinjana, Bothroyd, Johnson (Clarke 63).
Referee: H Webb (S Yorkshire).