Two first-half goals for the hosts gave Michael Laudrup's side an uphill task but he will have been buoyed by a debut strike from Jonathan de Guzman as the Swans were defeated
Michael Laudrup's side fell behind to an early Andre Akpan goal as the Texan rose to meet Luis Zapata's pinpoint cross after four minutes, planting his header past Gerhard Tremmel.
And though the Swans came close to finding a reply via Leon Britton's long-range effort, the Rapids doubled their lead in impressive fashion as Kamani Hill drilled a 25-yarder in off the post on the quarter of an hour mark.
This kicked the visitors into life and though striker Danny Graham squandered two decent chances – the best a shot on the turn that was well saved by Steward Ceus – they went into the break 2-0 down.
Laudrup made ten changes at half-time, taking off new man, Michu, and introducing two debutants in Chico and Jonathan de Guzman.
The Welsh side started the second period far stronger, falling into their natural possession game quicker than they did in the first-half but struggled to convert this into genuine chances in the first 15 minutes.
On the 72nd minute, Leroy Lita had Swansea's best chance as he met Ben Davies cross, but saw his powerful header into the ground bounce over the crossbar.
The improvement in possession saw some good work by Kemy Agustien, Luke Moore and Lita lead to a free-kick for the Swans 25 yards out. Canadian midfielder, de Guzman took responsibility for the set-piece and fired an excellent curling shot into the far corner to pull Laudrup's team back into the game.
However with just ten minutes remaining, Swansea couldn't find the second goal they needed to restore parity as the Rapids saw out the friendly to win 2-1.