Diomansy Kamara also grabbed his first Albion goal with Robert Earnshaw getting off the mark for the season as Bryan Robson's side comfortably saw off his former club.
Ellington, snapped up for a club record £3million from Wigan, opened the scoring against his home town club with a neat piece of finishing.
Kamara, who cost the club £1.5million from Italian side Modena, looked to have put the tie beyond the reach of battling Bradford when he doubled Albion's advantage with a close range header.
But Bradford were determined they would not go down without a fight and Steven Schumacher stunned Albion when he handed City a lifeline on the stroke of half time.
Bradford then took the game to Albion in the opening stages of the second half and built up a real head of steam but there was no end product for Colin Todd's side.
Albion were able to nullify their threat and Ellington ended their challenge with a cool 72nd minute chip before Earnshaw set the seal on their success five minutes later.
The only downside for Albion was the dismissal of Martin Albrechtsen eight minutes from time after his professional foul on Dean Windass.
As had been expected, Bradford threatened in the opening exchanges when the lively Ben Muirhead and Bobby Petta flashed shots wide and Schumacher was also out of luck from long range.
After facing the early storm, Albion took a stranglehold on the game with two goals in the space of nine minutes through Ellington and Kamara.
Ellington broke the deadlock in the 23rd minute when he used his pace to chase a long ball down the centre of the pitch.
Former Bradford skipper Darren Moore headed clear out of defence and Darren Carter then hooked the ball into the path of Ellington.
Ellington was being pursued by the Bradford duo of Mark Bower and Darren Holloway but had the pace and power to pull clear of the pair and finished off a smart move by drilling a low right-foot shot past the despairing dive of goalkeeper Russell Howarth.
The game then looked to be over in terms of a contest after 33 minutes when Kamara took full advantage of another piece of pin-point accuracy from Carter.
This time the former Birmingham City midfielder, who made the short move to The Hawthorns from St Andrews for £1.5million this summer, whipped in a right-wing free-kick.
Senegal international Kamara, who had spent last season on loan at Portsmouth, rose above the Bradford defence to head home.
When Bower then cleared off the line from Earnshaw after Howarth had spilled a Carter shot, Albion looked set to run riot.
But Albion were disrupted when Kamara was forced to limp off a minute before the interval and Bradford took full advantage to secure a lifeline in first-half stoppage time.
Right-back Holloway lifted an excellent cross into the Albion area and the alert Schumacher got to the ball first to steer a well placed header past Tomasz Kuszczak.
It gave Bradford's small army of travelling fans hope but City were unable breach the Albion rearguard for a second time.
Their resistance was finally ended 18 minutes from time when Ellington was released by substitute Nwankwo Kanu.
He only had Howarth to beat and lured the former Tranmere keeper off the line before cheekily chipping the ball over his head.
Bradford wilted after Ellington's second strike and Kanu was able to turn provider again to set up the unmarked Earnshaw who completed the rout by stabbing home from six yards.