Defeat left Hull two points from safety and needing to beat Manchester United at the KC Stadium on the final day of the season a week on Sunday, with other results also having to go their way, in order to stay up.
Sunderland, who have two games to play, are three points ahead of Hull but with an inferior goal difference.
Newcastle were left just two points in front of the Tigers after a 2-1 loss to QPR -- their ninth defeat in 10 games.
Aston Villa were thrashed 6-1 by Southampton, with Sadio Mane scoring the quickest hat-trick in Premier League history, but results elsewhere kept the Birmingham club in the top flight.
Mane took just two minutes and 56 seconds to complete his treble and surpass the previous Premier League hat-trick record of four minutes and 33 seconds set by Liverpool striker Robbie Fowler against Arsenal in 1994.
"Any idiot knows we didn't play well, they don't need telling," said Villa manager Tim Sherwood, whose side face holders Arsenal in the FA Cup final at Wembley on May 30.
Elsewhere, Steven Gerrard was denied a fairytale finish in his last match at Anfield as Liverpool fell 3-1 to Crystal Palace, while Everton beat West Ham 2-1 and Burnley and Stoke played out a goalless draw at Turf Moor.
Sunday sees second-placed Manchester City travel to Swansea while Arsenal face Manchester United in a clash between third and fourth at Old Trafford.
Champions Chelsea are at West Bromwich Albion on Monday.
-AAP