Winger Wright-Phillips ripped the Claret and Blue defence apart with some surging runs and it was he who earned a penalty that Elano scored to put City into a first half lead.
The England man sealed the game with a fine goal in the second half, slotting past Brad Friedel with just minutes remaining.
Villa fans travelled to Manchester looking for an immediate response from their side after they surrendered a two goal lead at home to Stoke on Sunday.
The Villans were facing a City side without Craig Bellamy, Micah Richards and Robinho, and the travelling faithful would have been fancying their side's chances on the back of a seven game winning streak away from home in the league.
Unfortunately for the large visiting following, what they saw was an horrendous first half performance followed by a toothless second half display.
Villa were on the backfoot from the off and they could have and should have been at least three down before the break with Stephen Ireland missing two good chances.
Wright-Phillips also went through on goal but could only manage to steer a shot wide from no more than eight yards out.
City were flying through the Villa defence at will and it wasn't long before their pressure told as Wright-Phillips again went eye to eye with Friedel, only to be tripped from behind by James Milner.
Headers
Penalty awarded, Milner booked Elano scored. It was no more than the hosts had deserved and from then on you could only see one winner.
The Claret and Blue fans were forced to endure chants of "Istanbul" from rival fans, which really rubbed salt into the wounds.
Martin O'Neill, of course, chose to rest players for the trip to Moscow last Thursday and consequently Villa were knocked out of a trophy that the fans were hopeful of winning.
City's faithful are still in with a shout of seeing their side triumph in the competition and they made their delight known.
Villa had left players out to focus on finishing in the Champions League places but in the first period they looked more bottom four than top four.
After the break they stepped up the work rate and with John Carew brought on for Curtis Davies, who had a shocker, it was City who were backpedalling.
Carlos Cuellar was switched to centre back alongside Zat Knight and James Milner went to right back with Emile Heskey playing on the right wing.
The changes made the world of difference with Cuellar winning headers that Davies simply wasn't and Gareth Barry soon had Villa's first effort on goal with a well placed volley that forced a good save from Shay Given.
The away side also had a succession of corners but they couldn't make City pay for sitting back on their lead.
Strange
Ashley Young enjoyed a couple of surging runs down the left but his final ball let him down until on moment of brilliance where he whipped a teasing ball across the six yard line.
Gabby Agbonlahor, who has been goal shy, to say the least, of late, somehow managed to miss the ball completely as he failed to decide whether to go with his head or his foot. Incidentally, a header into the empty net was the best option.
Villa's pressure then started to fade and City began to have more chances.
Substitute Ched Evans volleyed wide and Elano forced an amazing save from Friedel as the home side looked to seal a win.
After Cuellar sustained a head injury at a corner, he was forced off the pitch to be replaced by Craig Gardner, who was placed unusually at centre half.
Wright-Phillips obviously picked up on the strange change and after playing a neat one two with Ireland he attacked the Villa defence and curled in to finish the game.
That goal was the signal for Villa fans to flood out in their droves, knowing that their side are now just three points ahead of fifth placed Arsenal.
And with fixtures against Tottenham, Liverpool, Manchester United and Everton to come in the next month or so Villa may just be seeing their challenge for the Champions League fade away.
If Agbonlahor fails to regain his confidence and O'Neill doesn't learn that Cuellar must be played at centre half alongside Knight then fourth is an unrealistic finish.
But, fans will remain confident, as this season their side have managed to make a habit of doing the unexpected.