Kagisho Dikgacoi netted the winner eight minutes from time to fully punish Peter Whittingham's 69th-minute penalty miss for the Bluebirds.
Palace are now unbeaten at home in 10 matches and have a four-point cushion above the relegation zone.
Freedman said: "It's very pleasing to win a very hard-fought match. We certainly had to work hard for that. Any win is pleasing right now.
"The lads are buzzing in the dressing room. They've done well and stuck to the game plan throughout the match.
"I've got a team, substitutes, a squad and fans here that are all pulling in one direction. It's getting us through - everyone is. We're sticking to training, sticking to working hard and sticking to smiling and we're getting these hard-fought victories."
Source: PA
Source: PA