Swansea's 1-0 victory against Everton on Saturday, following Hull City's defeat at home against Sunderland, means the Welsh club are out of the relegation zone with two matches remaining.
Swansea, on 35 points, are now one point clear of Hull with two games remaining in the battle for survival.
Paul Clement's men then opted to sit back in the closing stages of the half, with even Llorente deep in his own territory, but appeared comfortable in ensuring they held a priceless lead at the interval.
Sigurdsson has scored two free kicks this season, including one in the last match against Manchester United - since his Premier League debut in January 2012, he has scored more free kicks than any other player (7).
The Swans have won four of their last six at home, but their record when hosting top-half teams reads just W1-D1-L6 so far.More news: Mahrez wants out of Leicester; Arsenal and Tottenham lead the chase
That's no excuse for supporters though and it's now the third game on the bounce they have failed to pick up all three points. They play before us so we will know their result.
"What it says to everyone is 'We have an opportunity, don't waste it,"' head coach Clement said after Fernando Llorente's first-half header had secured the points at the Liberty Stadium.
With just three Premier League matches remaining, Swansea City are in real danger of dropping down to the Championship, with the club now sitting 18th in the table, two points behind Hull City in 17th spot.
Ronald Koeman's team were beaten 1-0 at the Liberty Stadium, with Fernando Llorente's goal being the difference on the night.
"Swansea needed to win".More news: United States unemployment hits 4.4%, lowest in a decade
The Swans begun the game positively despite Everton coming into this one as favourites and by dictating play, they controlled the tempo and indeed their opponents.
As well as the Toffees visiting Wales this weekend, West Brom will travel to face a Swansea side that have taken nearly double the number of points at home as they have on the road.
"We are confident we can go anywhere and get a result with the form we're in".
Everton, without a win in three games overall, return to action next weekend with a home match against Watford. In order to achieve this, the team must close a six point gap on Manchester United, who now occupy fifth spot in the Premier League table.
Silva opened the scoring inside two minutes and was untouchable as City's conductor until he went off to a standing ovation in the 67th, while De Bruyne also scored and set up goals for center backs Vincent Kompany and Nicolas Otamendi.More news: White House says Trump did not prompt DOJ review of Comey
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