Paul Scharner and Chris Brunt put the Baggies into a 2-0 lead at Goodison Park before Everton's top goalscorer Tim Cahill pulled one back.
Everton's hopes of a fightback were dashed as Mikel Arteta was sent off for stamping and Somen Tchoyi and Youssouf Mulumbu, with aid of a Sylvain Distin deflection, finished them off.
Remarkably Mulumbu was then sent off himself for two bookings, the first for celebrating in the crowd and then for a bad tackle on Steven Pienaar.
It was the only blot on an otherwise excellent day for the visitors, who had been looking for a lift after collecting just one point in their previous five games.
Everton are now without a win in five and their frustration was summed up by Arteta, who could have no excuse for his dismissal for stamping on Gonzalo Jara.
Source: PA
Source: PA