Full-back Denton, 20, curled in a fine effort in the first half as the Whites won a second-straight away game.
Kemar Roofe hit the crossbar for Leeds as they pressed for a second.
The Hatters had chances to equalise but Jack Marriott twice squandered efforts when he was one-on-one with the goalkeeper.
Match ends, Luton Town 0, Leeds United 1.
Second Half ends, Luton Town 0, Leeds United 1.
Attempt missed. Isaac Vassell (Luton Town) header from the centre of the box misses to the right.
Attempt saved. Kemar Roofe (Leeds United) right footed shot from the centre of the box is saved in the bottom left corner.
Attempt missed. Souleymane Doukara (Leeds United) right footed shot from the right side of the box is too high.
Lewie Coyle (Leeds United) wins a free kick in the defensive half.
Foul by Isaac Vassell (Luton Town).
Attempt saved. Isaac Vassell (Luton Town) header from the centre of the box is saved in the top centre of the goal.
Corner,  Luton Town. Conceded by Lewie Coyle.
Attempt missed. Cameron McGeehan (Luton Town) right footed shot from outside the box is too high.
Attempt saved. Alex Mowatt (Leeds United) right footed shot from outside the box is saved in the top right corner.
Attempt blocked. Kemar Roofe (Leeds United) right footed shot from the centre of the box is blocked.
Foul by Alex Mowatt (Leeds United).
Pelly Ruddock (Luton Town) wins a free kick on the left wing.
Corner,  Luton Town. Conceded by Alex Mowatt.
Corner,  Leeds United. Conceded by John Mullins.
Attempt blocked. Souleymane Doukara (Leeds United) right footed shot from the right side of the box is blocked.
Attempt missed. Jack Marriott (Luton Town) right footed shot from the centre of the box is close, but misses to the right.
Corner,  Luton Town. Conceded by Tyler Denton.
Substitution, Luton Town. Isaac Vassell replaces Olly Lee.
Substitution, Leeds United. Liam Cooper replaces Pontus Jansson because of an injury.
Delay over. They are ready to continue.
Delay in match Pontus Jansson (Leeds United) because of an injury.
Attempt saved. Kemar Roofe (Leeds United) left footed shot from outside the box is saved in the top centre of the goal.
Attempt saved. Kemar Roofe (Leeds United) right footed shot from outside the box is saved in the centre of the goal.
Stuart Dallas (Leeds United) wins a free kick in the defensive half.
Foul by Cameron McGeehan (Luton Town).
Substitution, Leeds United. Alex Mowatt replaces Pablo Hernández.
Substitution, Luton Town. Pelly Ruddock replaces Danny Hylton.
Attempt missed. Glen Rea (Luton Town) right footed shot from outside the box is just a bit too high.
Corner,  Luton Town. Conceded by Sol Bamba.
Attempt blocked. Cameron McGeehan (Luton Town) right footed shot from outside the box is blocked.
Corner,  Luton Town. Conceded by Sol Bamba.
Attempt saved. Cameron McGeehan (Luton Town) right footed shot from outside the box is saved in the bottom left corner.
Lewie Coyle (Leeds United) is shown the yellow card for a bad foul.
Foul by Lewie Coyle (Leeds United).
Danny Hylton (Luton Town) wins a free kick in the attacking half.
Corner,  Leeds United. Conceded by John Mullins.
Attempt blocked. Stuart Dallas (Leeds United) left footed shot from outside the box is blocked.
Substitution, Leeds United. Kalvin Phillips replaces Luke Murphy.
Tyler Denton scored on his Leeds United debut as the Championship side progressed past Luton Town in the EFL Cup second round.