Although they picked up maximum points, Sunderland remain at the foot of the Premier League table with just 24 points from 35 games.
With Middlesbrough close to joining Sunderland in the Championship next season, the favourites to be the third relegated side are either Hull or Swansea. Swansea City are 1/5 to stay up in the Premier League this season.
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.
There was no doubting Clucas' determination to make an impact on the game, and he left something of an impression on Sunderland midfielder Didier Ndong with a late tackle that earned a booking. Next-to-last Middlesbrough is set to drop, too, on Monday. The pressure is on Hull City now as they've relinquished their place outside of the bottom-three.
Palace has 38 points, Swansea 35, and Hull 34.
The losing team has failed to score in 23 of the 29 league clashes between Hull and Sunderland.
West Brom ended their goal drought with a 2-2 draw at Burnley.
Jordan Ayew floated over a cross from the right and Llorente leaped highest at the far post, bundling the ball home with his left shoulder.
Hull City's Lazar Markovic lies injured, during the English Premier League soccer match between Hull City and Sunderland, at the KCOM Stadium, in Hull, England, Saturday May 6, 2017.
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Supporters hoped it would send a strong message to North Korea , amid global concern over the escalation of its nuclear programme. It is likely that any economic pressure will negatively affect China , which is North Korea's closest trading partner.
Seven points from their last three games (Stoke City, Manchester United, Everton) is a points return better than any other side 11th and below, and their impressive results to stellar clubs of late will be encouraging as they go into their penultimate game.
Hull boss Marco Silva had been unbeaten in his previous 41 home league games, a record dating back to his time in charge of Portuguese side Estoril in 2014 and encompassing spells with Sporting Lisbon and Olympiakos.
Sunderland were backed by 2,542 supporters at the KCOM Stadium, with the travelling support out-singing the home support for large periods of the 2-0 win over Hull City.
It was Hull's first home defeat under manager Marco Silva, who rued costly lapses in concentration but put on a fearless face ahead of what will be a tense home straight.
The result also was a boost for Middlesbrough, which stayed alive ahead of its trip to Chelsea on Monday.
Captain Vincent Kompany celebrates scoring Manchester City's second goal against Crystal Palace.
But goals from right- back Billy Jones, in the 69th minute, and Jermain Defoe in added time gave Sunderland victory.
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.
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