The Republic of Ireland international grabbed two well-taken strikes to keep Palace living in hope that they may reach the play-offs.
Luton, depleted through injuries and suspensions, never really got going and they had to thank an own goal from Palace defender Mark Hudson to level early in the second half.
But it got worse for Luton as a few minutes later Richard Langley got his marching orders after picking up two yellow cards.
Palace took advantage and Morrison, who fired the Eagles in front in first-half stoppage time, was left to restore Palace's lead with the winning goal 20 minutes from the end.
Up until Morrison's first goal, the fans were getting restless with an awful, boring first half.
Gabor Kiraly's long free-kick fell to James Scowcroft, who cleverly glanced the ball to Morrison, and he finished off superbly with a low 15-yard shot into the far corner.
Morrison had already missed two good chances early on but both his efforts went a yard outside the post.
Luton looked quite comfortable although they were not able to cause too much danger to the home side.
They were clearly looking forward to half-time but Morrison's stoppage-time goal changed all that and Luton needed to up the tempo when they came out for the second half.
Manager Mike Newell got the right response from his side within ten minutes of the turnaround.
Lewis Emanuel got forward to join the attack and swung over an awkward cross which bounced just in front of Hudson. Kiraly made a late call to collect the ball, but by then the ball struck the hip of the unfortunate Hudson and the ball dropped over the line into the empty net.
Two minutes later, Luton were down to ten after Langley fouled Matt Lawrence to get his second yellow of the afternoon.
Palace responded by putting players forward and Morrison completed a fine performance with another classic finish.
Danny Butterfield crossed from the right, the ball was headed on by Leon Cort and Morrison reacted first with a cracking finish from 12 yards out, giving Marlon Beresford no chance in the Luton goal.
The Hatters tried to hit back and things improved when Dean Morgan came on. The Luton substitute had the best of several useful chances but fired wide of an open goal with just five minutes left.