Needing to beat the Potters and hope Southampton were thrashed by Manchester City - with a 10-goal swing in the Swans' favour - to keep alive their faint hopes of staying up, the hosts took an early lead through Andy King but Stoke fought back to win 2-1 thanks to goals from Ndiaye and Crouch.
The demotion not only ends Swansea's seven years stay in the English topflight but it means Ghanaian brothers Andre and Jordan Ayew have equalled an infamous record.
The sons of the three-time African best, Abedi Pele, have become only the second pair of brothers in Premier League history to be relegated playing for the same team.
The first were Martin and Marcus Olsson at Blackburn Rovers in 2012.
The Ayew brothers joined up at Swansea midway through the season. Jordan had been part of the club since January 2017 and brother Andre rejoined from West Ham in January 2018.
He played 11 times in the remainder of the campaign, with Jordan making 38 appearances over the course of the season.
For Andre, this is the first time he has tasted relegation in his career while his younger brother has suffered three times.
Jordan first tasted the ignominy of the drop with French side Sochaux in 2014 when a 3-0 defeat against Evian - who had Ghanaian Jonathan Mensah on their books - condemned them to the lower tier.
A year later, Jordan moved to Aston Villa, whose terrible campaign ended with relegation as they finished last on the table with only 17 points. And now with Swansea.
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