Making his Whites debut at left back, Denton curled home a 23rd-minute peach from the edge of the area to put United in Wednesday night’s third round draw.
The victory also made it back to back wins for United head coach Garry Monk, who made 11 changes to the line up that started the 2-0 Champiosnhip win at Sheffield Wednesday on Saturday in readiness for this weekend’s trip to Nottingham Forest.
United made an immediate impression but the wrong one when Matt Grimes received a booking in just the first minute for clattering Jake Gray.
The same player then headed the game’s first chance over the bar after eight minutes as the Hatters began brightly.
United threatened for the first time after 11 minutes when Kemar Roofe almost weaved his way through on goal from an angle but his shot was blocked, as was the subsequent follow up attempt from Pablo Hernandez.
Olly Lee then lashed a 30-yard pile-driver over the bar before Luton’s Cameron McGeehan went the closest yet when powering a 25-yard free kick just over, following Sol Bamba’s foul on Danny Hlyton.
A Stuart Dallas effort was then deflected wide at the other end but Luton still looked the most likely team to score first until Denton produced a moment of magic on his full debut.
With 23 minutes on the clock, fine work from Grimes saw the ball played to Roofe who laid off to the young left back who then nonchalantly curled a 20-yard screamer into the top corner with the edge of his boot.
And only the crossbar then denied United their second goal just seven minutes later when Roofe’s powerful effort cannoned back into the area to Dallas who saw a follow-up effort parried away by Chistian Walton.
Luton’s early pressure had subsided but Marco Silvestri had to show strong hands ten minutes before the interval to tip a stinging effort from Jack Marriott over the bar.
United immediately countered from the resulting corner and Roofe fed Souleymane Doukara in on goal at an angle, only for Christian Walton to divert the striker’s effort away for a corner.
But Luton then squandered easily the game’s best chance yet shortly before the break when Bamba tried to play Marriott offside but misjudged his timing and allowed the Luton styiker clean through on goal.
Marriott rounded the on-rushing Silvestri who then fell over but the Hatters forward then spooned his 20-yard effort over the bar when a rolled in finish would have sufficed.
Dallas then blazed over from range as Leeds looked to respond but Luton had the final chance of the first half in injury time when Lee’s low effort from range forced Silvestri into a diving save.
Roofe then looked immediately lively after the interval but it was Doukara who had the half’s first effort on goal when he curled wide from the edge of the area.
Dallas was the next Whites player to threaten when his rising effort was deflected over as the game reached the hour mark.
But Luton showed they were still a threat just two minutes later when McGeehan’s 20-yard free-kick forced Silvestri into a brilliant diving save to force a corner.
Silvestri then produced an even better but similar save two minutes later to deny the same player whose stinging shot was destined for the far corner.
At the other end, Roofe’s low effort was well held by Walton before Luton then saw claims for a 77th-minute penalty waved away after Silvestri dived in on Hylton.
Sustained home pressure was beginning to grow and Marriott then squandered another golden opportunity when racing clear one on one with Silvestri, only to fire just wide of the right hand post.
United were under the cosh but the Whites began to press themselves with five minutes left as sub Alex Mowatt’s curling effort was saved by Walton.
But just one minute later the Hatters wasted another fine opportunity when McGeehan slammed a fine chance over from the edge of the box.
The Hatters were then given four minutes of injury time to force a draw and McGeehan’s header from a 91st-minute corner was directed straight at Silvestri.
At the other end, Doukara then blazed over before United missed a brilliant chance to score their second when Doukara fed Roofe who fired his effort straight at Walton from ten yards.
But Leeds had done enough to seal a victory and book their place in Wednesday night’s draw.
Leeds United: Silvestri, Coyle, Jansson (Cooper 74), Bamba, Denton, Murphy (Phillips 58), Grimes, Hernandez (Mowatt 68), Dallas, Roofe, Doukara. Subs not used: Green, Ayling, Sacko, Antonsson.
Luton Town: Walton, O’Donnell, Mullins, Rea, Potts, Lee (Vassell 75), McGeehan, Smith, Gray (Cook 55), Hylton (Mpanzu 66), Marriott. Subs not used: Cuthbert, McQuoid, King, Justin.
Referee: Kevin Johnson.
Attendance: 7,498 (1,510 Leeds).
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