With Burnley and QPR already demoted, Hull remained in the last drop spot after second-half goals from Nacer Chadli and Danny Rose secured a 2-0 victory for Tottenham Hotspur at White Hart Lane.
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.
Leicester, bottom of the table for 140 days, ensured they would be playing in the Premier League next term after a goalless draw with fellow strugglers Sunderland.
The Black Cats are now three points ahead of Hull but with an inferior goal difference.
They may need at least a point from their two remaining matches, against Arsenal in midweek and away to champions Chelsea next weekend, to beat the drop.
Newcastle, Sunderland’s north-east rivals, were left just two points ahead of Hull 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.
In north London, Chadli gave Spurs the lead in the 54th minute before Rose’s volley seven minutes later condemned Hull to defeat.
“You can’t come to Tottenham and create five or six good chances and not take one,” Hull manager Steve Bruce told Sky Sports.
But Bruce, a former Manchester United captain, added: “We have to believe we can beat Manchester United next week. Is there one final twist? Can we upset the apple cart? Let’s hope we can do it.”
Newcastle went ahead against QPR when French forward Emmanuel Riviere scored with a scuffed shot in the 24th minute at Loftus Road.
But Matt Phillips equalised in the 54th minute before Leroy Fer’s stunning 35-yard effort secured victory.
“Having lost, this is the best scenario with Hull losing,” said Newcastle boss John Carver. “There’s one game left and it’s a do or die situation.”
– Mane magic –
Earlier, 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.
The 23-year-old Senegal winger had no idea he had secured a place in the record books, telling BT Sport: “Really? It is the fastest Premier League hat-trick? The most important thing today is the victory.”
Mane started his goal-spree in the 13th minute when he tapped into an empty net after a fortunate deflection as he tried to round Villa goalkeeper Shay Given.
Just 84 seconds later Mane struck again when he latched onto a sloppy back pass from Villa defender Ron Vlaar and slotted past Given.
And he completed his remarkable feat with a fine first-time finish into the top corner from the edge of the penalty area.
Villa pulled a goal back on the stroke of half-time through Christian Benteke before Southampton striker Graziano Pelle completed the scoring nine minutes before the end at St Mary’s.
“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, Everton beat West Ham 2-1 thanks to goals from Leon Osman and Romelu Lukaku after Stewart Downing had given the Hammers a 62nd minute lead at Upton Park, while Burnley and Stoke played out a goalless draw at Turf Moor.
Saturday’s late kick-off match sees Liverpool captain Steven Gerrard bid farewell to Anfield when he plays his last home fixture, against Crystal Palace, before joining the Los Angeles Galaxy next season.
Sunday will help determine which two clubs join Chelsea in the group stage of the Champions League next season.
Second-placed Manchester City travel to Swansea while third-placed Arsenal, who have a game in hand, face fourth-placed Manchester United at Old Trafford.
Chelsea are away to West Bromwich Albion on Monday.