The Frenchman’s under-21 side will face Reading in the two-legged final of the competition following a topsy-turvy 3-2 win over the Clarets.
Sinan Bytyqi and Jordy Hiwula scored in the first-half either side of Burnley’s 25th minute equaliser to give the Blues a 2-1 half-time lead, before the visitors levelled with on 65.
However, Bytyqi scored his second goal of the game ten minutes later to put the game beyond a talented and obstinate Burnley outfit.
It was a return to the scene of City’s 6-0 slaying of Burnley’s bitter rivals Blackburn just eight days previous.
Leigh Sports Village certainly held special memories for Hiwula, who had helped himself to four goals on that occasion, before following that up with a brace in the 6-2 win over Sunderland at the Etihad Stadium on Friday.
He started alone up front - elsewhere, the line-up showed four changes from the team that took on the Black Cats.
Captain Marcos Lopes was rested, allowing Devante Cole to return, while Mathias Bossaerts, Ellis Plummer and Greg Leigh came in for Adam Drury, Jason Denayer and Angelino.
Vieira’s men have been beaten just once in 16 games at under-21 level but they were coming up against a side who had conquered Wigan, Crewe, Sunderland, Bolton and Exeter on their route to the last four.
Andy Farrell’s team represented dangerous opposition, considering they knocked out Manchester United in the FA Youth Cup last season and reached the semis of the same competition in 2012.
The Blues have opened the scoring inside five minutes and have gone on to score six in their last two encounters and they made another excellent start to this semi-final, taking the lead after just nine minutes.
Seko Fofana led the charge, breaking from midfield to lay the ball into Hiwula who played a slide rule pass onto the right side of the area for Bytyqi who slammed into the far corner definitively for his sixth goal of the season.
On the evidence of their recent form you might have expected a City onslaught after taking such an early lead but it was the visitors who scored the next goal 15 minutes later, replying through an excellent long-ranger by Cameron Dummigan.
The Burnley full-back took aim from 25 yards and laced a daisycutter into the bottom corner of the net, beyond Ian Lawlor’s outstretched hand.
City responded to the concession positively and YouTube star Fofana nearly added another long range golazo to his growing portfolio on 35 minutes but this time goalkeeper Danijel Nizic was equal to his 35 yard howitzer, tipping it wide of the target.
Burnley’s reprieve was short-lived, however, as the home side raided down the right side to set up Hiwula for his seventh goal in three games and his 19th of the campaign in all competitions.
Shay Facey fed in Bossaerts on the byline in behind the Clarets defence and the Belgian picked out the City no.9 in the middle, giving him the simplest of finishes from a couple of yards out.
From the downcast faces of the City players on their way off at the break, it was clear that the Blues were far from satisfied with their first-half performance, despite the narrow 2-1 lead they held.
Although they had enjoyed the majority of the possession, their usual telepathic cohesion was missing with final passes failing to find their targets and the inventiveness and dynamism of their work on and off the ball not up to their usual sky high standards.
With Vieira’s half-time team talk presumably still ringing in their ears, City made a strong start to the second period and could have extended their lead after 47 minutes when goalscorers Bytyqi and Hiwula combined but Jordy missed the target by inches after the Austrian had cut back for him to shoot.
Burnley proved that they were made of stubborn stuff all night long and they produced another equaliser after 64 minutes when Jamie Gilchrist volleyed home from a corner that the Blues couldn’t clear after two attempts.
EDS captain Lopes was brought on straight after that leveller to try and avoid extra-time and his impact was immediate, as he dovetailed neatly with fellow substitute Drury, who drilled in a cross that everyone but Bytyqi missed.
The Austrian arrived at the back post to thrash in the goal which finally ended Burnley’s resistance and set up a meeting with Reading in the final.
The first leg will be played on a date TBC.
