Results elsewhere meant that Palace were bumped down to second place in Group D as it stood at half-time, with Sheffield United topping the group with one better goal difference than Palace.
With that in mind, Palace came racing out the blocks after the restart, knowing that winning the second-half would see them through.
Captain Bell nearly clawed one back for Palace five minutes after the restart, but he saw his effort from inside the six-yard box cannon back off the crossbar after Dixon managed to square the ball across.
Palace managed to get a goal back just before the hour mark through Adler Nascimento. Joe Gibbard won the ball inside the Leeds half and drove towards goal, playing Dixon in with a great through ball. The striker cut the ball back across the face of goal and managed to pick out Nascimento who powered it into the roof of the net.
Though it was 4-2 to the hosts, Palace were going to top the group and qualify for the next round on goals scored. However, with 10-men, it wasn’t to be as Leeds notched a fifth goal with 15 minutes remaining.
Charlie Crew fired an effort on goal which took a big deflection off of second-half substitute Caleb Kporha, before nestling in the bottom corner of the net past a stranded Palace defence.
Brown, searching for a hat-trick, nearly secured it late on with a speculative long-range effort which bounced back out off the crossbar.
After four minutes of time added on, the referee blew his whistle to bring an end to proceedings. The result means Palace finish second in Group D and will not qualify to the next round of the U18 Premier League Cup as the best second-place side.
Leeds United: Mahady (Ombang, 10), Diboe (Dawber, 87), Toulson, Coleman, Debayo (Cresswell, 45), Buchan, McFadden (Vincent, 81), Crew, Thomas, Brown, Wilson.
Sub not used: Chadwick.
Crystal Palace: Shala, Barton (Agbinone, 68), Grante, Jemide, Williams, Bell (Marsh, 79), Gibbard, Mustapha (Cardines, 45), Socoliche (Kporha, 45), Dixon, Nascimento.
Sub not used: Hill