The Swans' poorly-timed slump continued on Saturday when they went a seventh league game in a row without win - going down 1-0 at Bournemouth - with results elsewhere seeing them slip back into the bottom three.
Carlos Carvalhal's men spurned chances and their failings in front of goal meant they remained very much in the mire.
Should Swansea beat Southampton then they would still need a point against Stoke on Sunday to stay up.
It was their first win in six games and ensured a fourth successive season in the Premier League, not that Howe thinks his side are becoming an established force.
Fraser then did well to clear a Fernandez header off his goalline before a good chance for Bournemouth as Lewis Cook headed Joshua King's cross just over the crossbar. Southampton are level on points with the Welsh side but are one place above them due to a superior goal difference. Swansea huffed and puffed, but Eddie Howe's late substitutions took the tempo out of the game - a good move from the Cherries boss - and Swansea succumb to a third straight defeat.
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Swansea battled in vain to overturn an early lead by the blues but failed to trouble the scoreboard for the 16th time in the league. An improved second half was a welcome sight for the home fans but it didn't quite improve enough, leaving the visitors heading South the happier team.
Back to "who will go down, who won't" and Huddersfield will need some favours from above as they travel to face the league champions, the 2017-18 champions Chelsea before hosting Arsene Wenger in his final Gunners bow. They won four of those games, losing just once. With 31 strikes in the league so far, the Egyptian's goals have helped the club in all competitions and been a real surprise in the world of football.
The Swans now have two huge games against Southampton and Stoke and now, there's simply no margin for error, but that's something Carvalhal's men have brought on themselves, you feel. Bournemouth will be able to drop into a five at the back formation if they are on the back foot. The Norweign striker has three goals in his last five games, giving him seven goals this season.
In the reverse fixture, Bournemouth and Swansea played to a scoreless draw.
The first of their two remaining games is against Southampton, in a clash which could decide the fates of both teams.