The Swans ended a testing Premier League season in 15th placed as Jordan Ayew's first goal for the club and Fernando Llorente's late volley earned a 2-1 victory West Brom at the Liberty.
Paul Clement's side had trailed to Jonny Evans' first-half header, but two goals with 14 minutes earned three hard-fought points for the hosts.
First, Ayew nodded home Llorente's header across goal to equaliser, before the Spaniard volleyed sub Luciano Narsingh's cross in the 86th minute.
victory, plus Watford's defeat to Manchester City, meant Clement's side finished the season in 15th place - seven points clear of the relegation zone - with 41 points.
That was some feat for a side that was in the bottom three only a few games ago, but 13 points from the last 15 on offer saw a hugely satisfying end to the season for the Swans.
In front of a jubilant crowd in perfect conditions at the Liberty, the opening half saw a number of half chances created by either side.
There was not the pressure on Clement's side that they had played under, so the shackles were off.
Though the visitors created the opening chance which saw Salomon Rondon head straight at Kristoffer Nordfeldt, the Swans then started to place their authority on the game.
Leroy Fer blasted over after racing onto Gylfi Sigurdsson's pass before Jordan Ayew's effort was blocked again after being set up by the Icelander.
At the other end, Nordfeldt had to save down low after Rondon latched onto a through ball before Fer and Federico Fernandez saw their efforts drop wide.
Another chance, which saw Fernandez nod wide from a Kyle Naughton cross, went by before the visitors took the lead.
With 33 minutes on the clock, Darren Fletcher's corner found Jonny Evans, and the centre-back headed past Nordfeldt from close range.
The Swans pushed for a reply before the break, with Naugton's stinging drive rising over from 25 yards, but the Baggies went into the interval with a slender lead.
The Swans continued their search of an equaliser after the break, but again it was the visitors who carved open the first chance.
Rondon got the better of a tussle with Fernandez, and he raced towards goal. But a superbly timed block from skipper Leon Britton denied the striker as he was letting rip.
The Swans, though, were left kicking themselves for wasting a glorious chance to level soon after.
Sigurdsson's corner was flicked on by Fer to Fernandez, but the centre-back glanced his header wide from four yards.
Mawson then headed wide another teasing Sigurdsson corner, before the Swans finally made up for their wastefulness.
With 72 minutes on the clock, Sigurdsson's free-kick found Llorente, and he nodded along goal for Jordan Ayew, the Ghanaian nodded home his first goal for the Swans.
That was good, but things got even better.
With four minutes left, the lively Ayew touched wide for sub Luciano Narsingh, and his cross was volleyed home by Llorente.
Hymns and Arias echoed around the Liberty Stadium, and it proved a fitting end to a testing season for the club as the whole squad and staff then walked around the pitch for a celebratory lap to thank the fans for their fantastic support throughout the campaign.
SWANS: Kristoffer Nordfeldt, Kyle Naughton, Federico Fernandez, Alfie Mawson, Martin Olsson, Leon Britton (capt, Luciano Narsingh, 66), Leroy Fer (Ki Sung-Yueng, 81), Tom Carroll, Jordan Ayew (Oli McBurnie, 90), Gylfi Sigurdsson, Fernando Llorente.
SUBS: Gerhard Tremmel, Jordi Amat, Stephen Kingsley, Jack Cork.
WEST BROM: Ben Foster, Allan Nyom, Craig Dawson, Jonny Evans, Marc Wilson (Jonathan Leko, 90), Chris Brunt, Claudio Yacob, Darren Fletcher (capt), Jake Livermore (James McClean, 79), James Morrison (Hal Robson-Kanu, 84), Soloman Rondon.
SUBS: Boaz Myhill, Kane Wilson, Sam Field, Nacer Chadli.