The hosts dominated affairs at the Liberty Stadium but looked set to be punished for a lack of cutting edge in the first half before influential midfielder Darren Pratley converted the vital breakthrough in the 43rd minute.
Swansea remained firmly in control and a quickfire penalty brace from Scott Sinclair on the hour mark made it a miserable start to life in the Eagles hot-seat for fans' favourite Freedman, who was promoted from caretaker boss on Tuesday after first choice Eddie Howe opted to stay with Bournemouth.
The writing was on the wall for Palace having lost 10 and won only one of their 13 away games going into an encounter against a Swans side boasting a home record only bettered by leaders QPR.
But these are not the kind of games which will decide third-bottom Palace's fate come the end of the season.
The big team news ahead of kick-off was the inclusion of striker Jermaine Easter on Palace's bench after he was recalled from his loan spell at Swansea on Thursday by parent club MK Dons, who had in turn sealed a permanent deal for him to become Freedman's first signing at Selhurst Park.
Mark Gower enjoyed the first opening of the game after seven minutes but could only head Nathan Dyer's lobbed right-wing cross over the bar.
And it was Swansea who made almost all of the first-half running, albeit without cutting the Palace rearguard open.
Dyer tested Julian Speroni at his near post before the Argentinian tipped over an effort from Luke Moore, who was making his league debut, as the game started to open up with half-hour gone.
Dorus de Vries was pretty much a spectator in the City goal but just as it appeared Swansea would fail to make their first-half dominance count, Pratley popped up with his fifth league goal of the campaign.
Sinclair played a neat one-two with Gower and got to the byline before squaring for the unmarked Pratley to wrongfoot Speroni from just behind the penalty spot.
Swansea started the second half immediately where they left the first and went in search of a killer second goal.
And they were rewarded in the 56th minute when Dyer' jinking run was ended by David Wright in the penalty area, although contact was minimal.
Sinclair stepped up to send Speroni the wrong way, and he got the chance to do so again from the spot just five minutes later - this time instead opting for the left corner.
The second spot-kick coming after Steffen Iversen handled Alan Tate's header from Gower.
Easter got his introduction as a result, and the Wales international was only denied a debut goal by a superb stop from De Vries when clean through.
The remaining minutes were played out at a decent tempo, considering the scoreline, and despite Palace's attempts to snatch a consolation it was Swansea who celebrated the final whistle boasting a conclusive triumph to climb up to second in the Championship.