But it was far from a brilliant performance by Iain Dowie's team that had suffered a humiliating defeat to rivals Brighton in midweek.
Burnley battled hard in the vain hope of securing a point but were not able to break down a strong Palace defence.
Palace's Marco Reich controlled the first half but the hosts had to wait 38 minutes before eventually making the breakthrough.
It proved to be the best move of the half as, after several passes, Reich made ground towards the left byline before floating over a perfect cross to the unmarked Jobi McAnuff at the far post. The ex-Cardiff midfielder headed the ball back into the goalmouth for Morrison to apply the finishing touch from just a few yards out.
Earlier Burnley had Brian Jensen to thank for keeping them level. The Danish keeper made fine saves to deny Ben Watson, Morrison and Reich as Palace put their foot on the gas.
But Burnley had a few half-chances themselves as John Spicer and Garreth O'Connor forced Eagles keeper Gabor Kiraly to make two diving stops.
However, the Hungarian keeper made his best save when he palmed away a well-struck 20-yard free-kick from O'Connor which looked certain to find the net.
After the break Palace took their foot off the pedal and allowed Burnley to get back into the match.
John McGreal fired in a low shot which Kiraly saved at full stretch and former Palace man Ade Akinbiyi produced a powerful header which flew a whisker wide of the post.
At the other end Reich curled a shot just over the bar after Watson had split the Clarets defence with a well-measured pass.
Just 12 minutes from the end Freedman scored his first goal of the season to finally kill off Burnley's hopes of securing a point.
Substitute Wayne Andrews riffled a shot from the edge of the box which was too hot for Jensen to make a clean save. Morrison did well to keep the ball in play and waited a few seconds for Freedman to move into the six-yard box to score with a rising shot.