Ellington, who has struggled to make an impact with Albion since his arrival from Wigan in August, struck with a first-half penalty and a curling 69th-minute shot to help secure Albion's biggest ever win in the Premiership.
His spot-kick opener also ended goal Albion's drought after five hours and 29 minutes of goalless Premiership action.
Albion put the game out of reach of a poor Everton side six minutes into the second half when central defender Neil Clement headed home a Diomansy Kamara corner.
Ellington grabbed his second 21 minutes from time before substitute Robert Earnshaw struck in stoppage-time.
The win also moved Albion out of the bottom three at the expense of Everton, whose recent resurgence came to an embarrassing halt.
The visitors never got into gear against Albion and James Beattie failed to reproduce the form that had seen him score three times in the last five games and he was hauled off after 63 minutes and replaced by Duncan Ferguson.
Everton's problems in attack were perfectly summed up by the fact that their best chance to score came when Albion's Japanese midfielder Junichi Inamoto deflected a 61st-minute Andy van der Meyde free-kick towards his own goal - forcing a brilliant one-handed save from Tomasz Kuszczak.
Albion should have been in control of affairs well before Ellington broke his Premiership duck with a coolly taken penalty.
They dominated the majority of the first-half but did not find a way through the determined Everton defence until Ellington's injury-time strike.
Visiting keeper Nigel Matyn was in fine form to deny Ellington, twice, and Inamoto as the Baggies piled on the pressure.
The Toffees sprang to life in a two-minute spell that saw van der Meyde and Bent head over the crossbar.
The misses proved costly when, on the stroke of half-time, Ellington was sent clear by Kanu, only to be sent sprawling by Tony Hibbert's careless challenge.
The foul looked to have been outside the box, but referee Dermot Gallagher pointed to the spot and Ellington made no mistake.
There was nothing controversial about Clement's header for Albion's second. A surging run by Kanu earned the corner that Kamara floated over for Clement to power home from six yards out.
Kanu, who had replaced the injured Geoff Horsfield in the 35th minute, was again the provider in the 69th minute, rolling the ball across the edge of the Everton area for Ellington to curl home left-footed from 20 yards.
To add insult to injury for the Toffees, Earnshaw, who had only been on the pitch for four minutes, marked the 250th appearance of his career with a smart finish from the edge of the area after racing on to a mis-placed back pass by David Weir.
Man of the Match: Kanu
The Nigerian striker failed to get on the scoresheet but set up three of the goals with some sublime pieces of skill, to underline his importance to the side.