LONDON (REUTERS) - The battle to avoid Premier League relegation took a significant twist on Saturday (May 6) as Swansea City capitalised on Hull's defeat to Sunderland with a victory against Everton allowing them to leapfrog the Yorkshire side into 17th place with two games left.

After relegated Sunderland had taken a surprise 2-0 victory at Hull, Fernando Llorente headed the solitary goal as Swansea held on to register a nervous victory and climb out of the bottom three for the first time since March.

Four consecutive home wins had put Hull's fate firmly in their own hands but, given the chance to pull five points clear of third-from-bottom Swansea City, they suffered an attack of the jitters that could prove fatal.

Second-half goals by Billy Jones and Jermain Defoe earned bottom club Sunderland a first win in 11 games and condemned Hull to a first home defeat under Marco Silva.

"It's disappointing," Hull manager Marco Silva told the BBC.

"We had chances to score in many moments of the game. Ultimately there was big tension in some of the team. We need to be calm in some moments.

"It's an important moment for us. We didn't achieve what we wanted from the match but we have two more games."

Swansea knew a victory in the late kickoff would see them leapfrog Silva's side and, after Llorente's goal, the Swans defended stoically until the final whistle prompted a mass outpouring of relief.

"Today was very important to move from 18th. I am very happy because this win is so important. It's a massive three points and now it depends on us," Llorente told BT Sport. "We need to win the two games we have left and this is the way we can do it."

Champions Leicester City finally ensured their safety with a 3-0 victory at home to Watford, while Stoke City and Bournemouth will be playing top-flight football next season after a 2-2 draw on the south coast.