Kyle Naughton's first goal in more than six years helped Swansea to the brink of Premier League safety as relegated Sunderland capitulated horribly.
Naughton's piledriver in first-half injury time coupled with Fernando Llorente's early header eased the Welsh club to a 2-0 victory and four points clear of Hull with a better goal difference.
And Paul Clement's men will stay up if the Tigers lose at Crystal Palace on Sunday.
They have taken 10 points from the last 12 available just when they needed it most, in stark contrast to the Black Cats, whose win at the KCOM Stadium last weekend proved to be yet another false dawn, and manager David Moyes was subjected to sustained calls for his head with owner Ellis Short watching from the stands.