A late Glenn Murray penalty ensured Palace's long journey to south Wales was worth it as they secured another valuable Premier League point at the Liberty Stadium.
In a real game of two-halves, Jonathan de Guzman had given Swansea the lead halfway through the first-half and the hosts looked in cruise control until the break, but the introduction of Murray helped turn the tide and he netted his first top-flight goal after being brought down by Chico Flores who was red-carded with eight minutes remaining.
The explosive conclusion was in contrast to the game's beginning, which started in the midst of a traditional Welsh downpour and the opening 20 minutes were a damp squib as neither side managed a shot in anger, and as unsurprising as the weather conditions was Swansea dominating the possession stats.
However the first attempt at goal fell to Palace when Marouane Chamakh headed tamely at Michel Vorm before the hosts replied when Pablo Hernandez saw a fizzing drive flash past the far post in what was his last action before being subbed for Jose Canas after picking up an early knock.
But on 25 minutes the Swans made their passing dominance count by netting the opening goal. Ashley Williams found Wilfried Bony who held the ball up for Leon Britton, and the diminutive winger slotted a perfect pass into the path of de Guzman who had broken from deep, and the Dutchman had time to take a touch before coolly rolling the ball past Julian Speroni.
The news got worse for Palace when top scorer Chamakh was forced off with a hamstring problem just after the half hour mark, and only some brilliant reactions from Speroni prevented the Eagles falling further behind when he denied Bony at point-blank range after another slick passing move involving Wayne Routledge and Angel Rangel.
Murray was introduced at the break as the Eagles pushed another striker up front and the switch in formation seemed to help invigorate them after a tepid first-half. Yannick Bolasie screwed a half-chance well wide of the target and Murray hooked a shot towards goal after a Cameron Jerome knock-down as the visitors bossed the second period.
With time ticking away Tony Pulis' side pushed forward much more often with the Swans visibly tiring after their European exploits just 72 hours previous, and Jerome connected with a wicked delivery from Jerome Thomas but his header couldn't trouble Vorm.
But the game turned on it's head with nine minutes to go. A loose long ball caught out Vorm and Murray poked the ball past the keeper before being hauled down by Flores. Replays showed the contact was outside the area but Mike Dean pointed to the spot before dismissing the defender and Murray dispatched the spot-kick to equalise.
Minutes later and Murray was almost celebrating again when a Bolaise centre deflected into his path but Rangel did well to block his goalbound effort, and after plenty of late pressure which saw Bolasie narrowly miss the target in injury-time, the point was the least Pulis' boys deserved for their second-half display.
Swansea City: Vorm, Rangel, Chico, Williams (Amat 70), Davies, Britton, de Guzman, Dyer, Hernandez (Canas 22), Routledge, Bony (Lita 63). Subs not used: Tremmel, Taylor, Emnes, Vazquez.
Palace: Speroni, Ward, Dann, Delaney, Parr (Thomas 70), Dikgacoi, Jedinak, Bolasie, Ledley, Ince (Murray 46), Chamakh (Jerome 32). Subs not used: Hennessey, Gabbidon, Bannan, Thomas, Gayle.