The Reds led at the break through Lukaku's neat finish and doubled the advantage when the Belgian hooked home superbly, following headers by Chris Smalling and Victor Lindelof.
Although Joel Ward pulled one back with a diving header, skipper Young made the points safe with a firm finish from a tight angle in the closing stages.
Solskjaer was forced to make three changes to the side that drew 0-0 with Liverpool on Sunday. Fred, Diogo Dalot and Alexis Sanchez came in for injured trio Ander Herrera, Juan Mata and Marcus Rashford, though the latter recovered enough for a place on the bench.