The Scottish hit-man pounced after Shaun Derry's inswinging corner was flicked on by Andrew Johnson leaving Freedman with the simple task of forcing the ball over the goal-line.
It finished off a poor Easter for the Hammers who just can't seem to find the net these days.
They gave Palace few worries although David Connolly did not help by collecting two yellows to be sent off nine minutes before the break.
Ironically West Ham's best chances occurred immediately after Connolly was sent off when Christian Dailly fired over an open goal and Marlon Harewood mishit a glaring opportunity with the goal in front of him.
A spicy match played at a frantic pace saw Tomas Repka, Chris Cohen and Bobby Zamora all booked as well as the Connolly sending off while Tony Popovic was cautioned for Palace.
Crystal Palace took a firm grip after the break. Julian Gray, Palace's best player, fired over before Freedman's goal and from then on the Eagles wasted chance after chance as Gray again went close. Johnson also fluffed a couple of one-on-ones with Pavel Srnicek.
Palace were rock-solid although really there wasn't any creativeness or finishing power from West Ham to stop Palace securing their third consecutive win.
Hammers boss Alan Pardew said afterwards: "The sending off was harsh as Connolly didn't deserve the second yellow but when you are down to ten men what can you do apart from trying to win every goal.
"Our away from is not looking good and confidence is lacking."
Palace boss Dowie said: "It was a great team effort against a quality side. The second half was a one-sided game and there were a lot of good performances out there from my lads. We deserved our win.
"Connolly did foul Danny Butterfield but whether it was bookable is another matter."
Crystal Palace: Vaesen, Granville, Popovic, Hudson, Butterfield, Gray, Hughes, Riihilahti, Routledge, Johnson, Freedman. Subs: Derry, Black, Leigertwood, Soares, Berthelin.
West Ham: Srnicek, Ferdinand, Repka, Dailly, Harley, McAnuff, Reo-Coker, Mullins, Horlock, Harewood, Connolly. Subs: Melville, Zamora, Deane, Cohen, Forde.
Referee: A Bates (Staffordshire).