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 Swans went ahead just before the break when Mark Gower got to the byline before squaring for Pratley to wrongfoot Julian Speroni from just behind the penalty spot.
Swansea were rewarded with a second goal in the 56th minute when Dyer's jinking run was ended by David Wright in the penalty area, although contact was minimal and Sinclair stepped up to send Speroni the wrong way.
Sinclair 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 was awarded after Steffen Iversen handled Alan Tate's header.