The Republic of Ireland international volleyed home ten minutes after the break to give Palace their second consecutive win and ensured Coventry's misery continued on the road.
And the Sky Blues were not helped by the sending off of defender David McNamee for a second bookable offence following a foul on Jobi McAnuff.
The first half was not particularly good with both sides struggling for passes despite perfect conditions on a warm afternoon.
The nearest Palace came to scoring came on the half-hour when Leon Cort rose high to head across the goal-line with Morrison just failing to finish off as Coventry scrambled clear.
Other than that, McAnuff had a couple of half-chances while Morrison volleyed over from James Scowcroft's pass.
Coventry had one excellent chance when Elliott Ward headed wide from Stephen Hughes' inswinging free-kick.
After the break, Palace looked a bit brighter and got their reward within ten minutes. Captain Michael Hughes on the right touchline drifted inside and passed to Mark Kennedy who in turn kept the move ticking with Gary Borrowdale overlapping.
The England Under-21 full-back swept over an awkward cross but Morrison brilliantly chested it down onto his left foot and from 15 yards out by-passed Andy Marshall as the ball flew into the top corner.
Darren Ward and Cort were giving nothing away as Coventry tried to get back. But their hopes disappeared after McNamee made a rash challenge on McAnuff and referee Mr Woolmer, who had a fussy afternoon anyway, flashed his yellow card at him for the second time.
Palace should have added a second near the end when substitute Shefki Kuqi won the ball from keeper Andy Marshall wide on the left touchline.
The Finland striker then unselfishly passed across the pitch to Morrison who, from 40 yards out and with an open goal in front of him, placed his shot over the crossbar.