With the Swans now 17th in the table, just three points clear of the drop and Southampton, a win would do them a world of good in going further clear of the Saints, who face Everton on Saturday evening at Goodison Park.
The Welsh club face 18th placed Southampton next Tuesday in arguably their most important game of the season, but will first need a positive result against the Cherries if they are to pull off the great escape for a second season in a row.
Yet Swansea struggled to take inspiration from their goalkeeper's heroics and now find themselves relying on results elsewhere to become only the fourth side to survive the drop who were bottom of the Premier League at Christmas.
Carlos Carvalhal's men spurned several chances but their failings in front of goal meant they remained very much in the relegation mire.
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Carvalhal's main improvement has been an increase in attacking output from Swansea.
Bournemouth failed to respond and were lucky not to be trailing by more before Josh King restored parity on the stroke of half-time. 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.
The two lasted the entire duration of the game which Swansea needed to win to all but ensure their safety. We didn't compete enough for the second ball.
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At least 88 of them have been allowed into the United States thus far, but dozens more are still waiting at the border. More than 11,000 people across Central America died and millions were left homeless in the wake of the storm.
"When we arrived if I would have said we have two games to finish the season and it would be possible to stay in the Premier then no one would have believed me". They believe, we believe, and together we can go on to secure our Premier League status.
BC-SOC- Bournemouth-Swansea, 233 Swansea not safe yet after losing at Bournemouth 1-0 in EPLAP Photo LON854, LON838, LON842Eds: With AP Photos.
These sides played out a scoreless draw in the reverse fixture at St Mary's Stadium back in August, while Southampton have won six of the 11 Premier League matches between these clubs.
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The first of Swansea's two remaining games is against Southampton, in a clash which could decide the fates of both teams.