Despite carving open a host of chances, City had to wait until the 64th minute before Liam Delap made the all-important breakthrough, the striker converting from close range after fine work by Morgan Rogers.
The victory means Gareth Taylor’s side, who are still unbeaten in 2020, continue to go from strength to strength, having already sealed a place in next week’s Premier League Under-18 Cup final.
With Burnley’s propensity for long balls mixed with a physicality in the air, it made for a different type of challenge for Taylor’s charges.
And with the visitors also employing a high press, it meant space and time was at a premium.
However, City’s patience in possession and fluid movement soon saw us on the front-foot.
But despite creating a litany of chances it was to prove a frustrating first 45 minutes as we sought in vain to apply a finishing touch to round off some impressive build-up play.
The pattern for that opening half was set on three minutes when an inswinging Tommy Doyle corner was met by Rogers on the half volley but his effort was too high.
More excellent approach work then saw Jayden Braaf create an opening before whipping in a low shot which just evaded the target.
Palmer then warmed Burnley keeper Harry Allen’s gloves with a vicious effort from the left side of the box, the rebound just avoiding the onrushing Doyle.
Braaf was the next to go close. His mazy run leading the Burnley defence a merry dance before the Dutch winger cut inside only to see Allen smother his shot.
And Allen was called into action again on the half hour, clawing away a curling Doyle shot.
Palmer then produced another moment of magic, jinking past Kane Patterson on the left before drilling in a low cross with Burnley skipper Chris Conn-Clarke sliding in to deny Doyle.
The pattern of dominance continued after the break with Palmer steering a 55th minute Doyle free-kick inches wide of the far post.
And to compound City’s frustration, when Delap did finally apply the finish from Doyle’s shot-come-cross, the linesman’s flag was raised for offside.
However, Delap was not to be denied and on 64 minutes both his and City’s endeavour was finally rewarded.
Hodge’s intelligent ball set Rogers free on the left who, in turn, found the waiting Delap who finished with aplomb.
With Burnley forced to deploy more men forward, only a smart Allen save stopped Braaf doubling our advantage with a powerful drive.
However, there was almost a moment of calamity on 80 minutes when keeper Cieran Slicker misjudged a McDonald pass on his goal line and Max Thompson saw his interception fly just wide.
Despite that scare though, City saw the job through to deservedly move into the last four.
What it means
City can now look forward to a semi-final encounter against either Arsenal or Blackburn Rovers who meet in their quarter-final clash in Lancashire on Friday evening.
The date and venue for the semi-final will be announced in due course.
How we lined up
Cieran Slicker was in goal shielded by a back four of Alpha Diounkou, Rowan McDonald, Taylor Harwood-Bellis and Josh Wilson-Esbrand. Joe Hodge was the midfield anchor with skipper Tommy Doyle and Cole Palmer also in the engine room. Liam Delap operated as the striking spearhead with Jayden Braaf and Morgan Rogers deployed on either wing.
Gareth Taylor’s youngsters are back in action next Tuesday, March 10, for another huge Cup encounter.
We play host to Stoke City Under 18s in the Under 18 Premier League Cup final, where we will be looking to defend the trophy we won 12 months ago.
Kick-off at the Academy Stadium is 7.45pm.