Goals from Crysencio Summerville, Liam McCarron and Sean McGurk, against a side who lost a man to a red card on 20 minutes, did the damage for Mark Jackson's men.
Goalkeeper Kristoffer Klaesson, midfielder Lewis Bate and winger Amari Miller made their Premier League 2 debut for Leeds against their fellow newly promoted side.
Adam Forshaw was given another minutes of action as he continues the road back to first team football after 23 months out, partnering Bate and Jack Jenkins in the middle of the park.
The Whites endured a difficult first few minutes, Klaesson struggling with his distribution as Palace pressed with intensity, but on seven minutes Leeds were ahead.
Bate nipped in to win the ball, Jenkins swung it to the right and Crysencio Summerville controlled expertly to beat his marker, enter the penalty area and slot the opener past Joe Whitworth.
Four minutes later parity was restored as a corner was headed in, unmarked, by Eagles centre-half Jake O'Brien.
The game took a dramatic turn before the 20 minute mark, Leeds fashioning a golden goalscoring opportunity, Joe Gelhardt' s blocked shot falling for Miller who sent the ball goalward only for David Boateng to block it on the line with his arm.
A red card was produced, Boateng walked and Gelhardt stepped up to see a tame spot-kick saved by Whitworth. The goalkeeper was instrumental in keeping the scoreline 1-1, throwing himself through the air to claw Cody Drameh's deflected cross away from his net.
Drameh and Summerville shone in a first half Leeds went on to dominate, Palace falling back and defending deep but struggling to prevent the visiting right-sided duo from getting into the area to cause problems.
Sean McGurk replaced Summerville at the interval, with Nohan Kenneh taking Charlie Cresswell's place at centre-half, the captain having picked up a booking for his part in a first half shoving match. Kenneh took little time to join Cresswell in the book, engaging in a nose-to-nose confrontation of his own early in the second half.
Leeds lost a little of their control after the hour mark when Forshaw departed to be replaced by Greenwood, Klaesson forced into a couple of saves, but the Whites were soon back on top and shortly after Gelhardt went close from an acute angle, the visitors were ahead.
A nice team move worked the ball to the right flank where Drameh got to the byline and flashed the ball across the goalmouth for his fellow full-back Liam McCarron to arrive and crash home for a 2-1 lead with 20 minutes left.
The third goal arrived when Jack Jenkins' lovely forward pass was cut back from the byline by Miller, his cross to the back post controlled and drilled into the net by McGurk.
Klaesson got in on the action in the late stages, saving David Omilabu's penalty after Drameh's foul in the area, then tipping a long-range effort over his bar with an equally good stop. Robert Street forced the Norwegian into another sharp save deep in stoppage time, before Gelhardt squandered a chance to add Leeds' fourth at the end of a dangerous counter attack, the striker trying to beat one man too many in a packed area.
The game ran to 97 minutes before the full-time whistle brought to a close a highly satisfactory start to the season for the 23s.