The former Arsenal man struck shortly before the hour to complete what has been a highly impressive second half of the season for the London club
The Moroccan scored Palace's first home goal of the campaign in a 3-1 defeat to West Ham in August, but had failed to find the net in the top flight since.
Chamakh, though, proved the difference between the sides on Sunday, converting a close-range effort after 57 minutes to move Palace to a final tally of 48 points – their record for a 38-game Premier League season - and a top-10 finish.
The 31-year-old did not last long after finding the net, though, as he pulled up with a hamstring problem seven minutes later.
Swansea's threat was limited throughout, but Garry Monk can reflect on his own record-breaking first full season in charge at the Liberty Stadium.
The visitors were boosted by the early return of Kyle Naughton from an ankle injury – one of four changes as Monk rested the likes of captain Ashley Williams and Gylfi Sigurdsson – while Wilfried Zaha was rewarded for his goal in a 3-1 win at Liverpool last weekend as one of three additions to the Palace starting XI.
And it was the former Manchester United attacker who caused the early threat but his close-range shot was charged down by ex-Palace loanee Jazz Richards, which afforded goalkeeper Lukasz Fabianski a comfortable save.
Jack Cork stuck his neck out to force Wayne Hennessey into a save at his near post from a corner, although it was Palace who continued to look most likely to break the deadlock – Zaha again sending a weak effort on target before Swansea scrambled away when a Yannick Bolasie drive proved too hot for Fabianski to handle.
Bolasie tried his luck again 10 minutes from the interval, but his 20-yard strike drifted over via the head of Federico Fernandez.
Hennessey got his body behind the ball to keep out a Marvin Emnes effort at the beginning of the second period, while Glenn Murray – a first-half replacement for James McArthur – failed to really test Fabianski with a header at the other end.
But Chamakh had the Pole beaten three minutes from the hour mark as Palace converted a set-piece opportunity.
The former Arsenal frontman controlled well from Scott Dann's header across the box to poke home after shaking off marker Bafetimbi Gomis.
That proved to be Chamakh's last contribution before being forced from the field through injury, although Zaha and Jason Puncheon both went close to adding to their stricken colleague's opener, Fabianski showing strong hands to deny the latter.
Monk introduced youngster Kenji Gorre for a Swansea debut late on, but the Dutchman was unable to spark a turnaround for the visitors, although the Welshmen can still look back at a season of success, having finished eighth, their highest Premier League placing.
IN PICTURES The final day of the 2014-15 Premier League season