Whites midfielders Eirik Bakke and Seth Johnson made another step towards a first team return by playing an hour each and Icelandic international Gylfi Einarsson played his first game after the effects of a dead leg he suffered in training and he had a good 70 minutes or so.
Darlington had plenty of experienced first teamers in their side, including Michael Price in goal, Chris Hughes, Joe Kendrick, David McGurk, Clark Keltie and Mark Convery.
United started off brightly but the Quakers took the lead when Parkin scored with a shot inside the far post.
Then Hughes made a bad tackle on Martin Woods and was ticked off by the referee.
Darlington then made it 2-0 five minutes after the break when Convery lofted the ball into the net.
Convery then hit the post with a header from a cross by St Juste.
Craig Russell made it three on 67 minutes to complete the scoring.
But Leeds would have been pleased with the performances of Bakke, Johnson and Einarsson.