Ghanaian international Andre Ayew’s winner on Saturday against Everton ensured Francesco Guidolin’s reign as Swansea head coach began on an impressive note.
The Italian oversaw an improved display from the Swans, who led through Gylfi Sigurdsson’s penalty.
The hosts levelled when Gareth Barry’s near-post flick from a corner was touched into his own net by Jack Cork but Ayew’s deflected strike won it.
Everton missed a host of chances, the best of which Seamus Coleman put over from six yards with the final kick.
This was the Welsh side’s first league win over Everton but, more importantly, it is the first time they have managed successive victories in the Premier League this season, adding to Monday’s 1-0 home success over Watford.
They are up to 15th in the table and now have a cushion between themselves and Newcastle in 18th and a momentum that eludes their relegation rivals.
It is another disappointing result for the Toffees, who twice threw away a lead to draw at Chelsea last weekend and have now won just three of their past 14 matches at Goodison Park and one win in 10 league matches overall.
They are 12th in the table having gone into the campaign hoping to improve on last season’s 11th-placed finish.