* Swansea City climb out bottom three with 1-0 Everton win
* Fernando Llorente headed Swansea ahead after 28 minutes
* Everton dominated possession but Swansea defended stoutly
* Swansea one point above Hull City with two games remaining
* Swansea visit relegated Sunderland next, Everton host Watford
May 6 (Reuters) - Swansea City climbed out of the Premier League's relegation zone with a 1-0 win against Everton on Saturday giving their survival aspirations a significant boost.
After Hull City suffered a surprise 2-0 defeat against relegated Sunderland earlier in the day, Fernando Llorente's first half header sealed a precious win for the Welsh side.
The Swans defended resiliently for large periods of the second half but could have extended their lead, and eased the growing tension around the Liberty Stadium, had Llorente and Leroy Fer done better with promising chances amidst the Everton pressure.
Swansea, who have 35 points, face bottom-of-the-table Sunderland and West Bromwich Albion in their final two games while Hull, on 34 points, play Crystal Palace and finish with a difficult game against Tottenham Hotspur.
Everton sit seventh with 58 points from 36 games. (Reporting By Tom Hayward, editing by Pritha Sarkar)