Tom Davies scored deep into added time as Everton salvaged a 1-1 draw against 10-man Southampton at Goodison Park, preventing their opponents from escaping the Premier League relegation zone.
Southampton's Ryan Bertrand kept the ball in bounds, but Everton's Idrissa Gueye collected it near midfield and sent it up to Davis at the top of the area. His shot, in the 96th minute, went off the inside of Wesley Hoedt's left leg and past a stunned goalkeeper Alex McCarthy.
Nathan Redmond, a half-time substitute who had not scored in nearly a year, put the visitors ahead in the 56th minute when he headed home through Jordan Pickford's legs from a cross by Cedric Soares, but Southampton were reduced to 10 men when Maya Yoshida was shown a straight red card for taking down Niasse in the 85th minute.
The draw reduced Southampton's survival hopes, with a six-point game against relegation rivals Swansea City looming on Tuesday.
It also meant that West Bromwich Albion, who defeated visiting Tottenham Hotspur 1-0 on Jake Livermore's 93rd-minute stunner, have temporarily warded off joining Stoke City in the Championship next season.
It was their fifth game without defeat under caretaker manager Darren Moore, who steered his club to a victory over Manchester United in his second game and a late draw against Liverpool in his third.
Tottenham began the day one point behind Champions League finalists Liverpool, who will visit fifth-place Chelsea, six points behind Spurs, on Sunday.
Spurs controlled the game for much of the first half, allowing only one real chance for West Brom, and Livermore broke through in added time despite Moore having removed both of his forwards by the 80th minute.
West Ham United strengthened their bid for survival with a 2-0 victory over Leicester City at the King Power Stadium, ending a run of four games without a win.
Joao Mario fired West Ham in front in the 34th minute when Marko Arnautovic hit the crossbar off a set piece and Joao Mario finished from the centre of the box.
Captain Mark Noble then doubled the lead in the 63rd minute when Leicester's Aleksandar Dragovic failed to clear a free kick with a header that led to a thundering volley from 25 yards that skipped past diving goalkeeper Ben Hamer.
Goals from Roberto Pereyra and Andre Gray ensured Watford will remain in the Premier League with a 2-1 victory over Newcastle United at Vicarage Road.
Watford had not won since March 3, a run of seven games without a victory, and had not scored multiple goals in a victory since Feb. 5.
Pereyra scored the opener in the second minute on a low-footed drive into the bottom right corner from 10 yards, and Gray doubled the lead in the 28th minute with a header from very close range on Pereyra's cross.
Newcastle goalkeeper Martin Dubravka prevented a third goal in the 39th minute when he saved Troy Deeney's penalty, awarded after Paul Dummett fouled Gray in the area.
Ayoze Perez pulled one back in the 55th minute, but Newcastle were unable to equalise.
Peyera's goal was Watford's first since he scored in the 61st minute of a loss to Burnley on April 7.
Bournemouth secured their place in the Premier League next season with a 1-0 victory against Swansea City after Ryan Fraser's 34th-minute goal.
Callum Wilson was fouled just outside of the penalty area and Andrew Surman's restart ended up at Fraser's feet, with the midfielder's shot deflecting past Swansea goalkeeper Lukasz Fabianski.
Swansea, still in the drop zone, will face relegation rivals Southampton in a crucial Tuesday game.
Earlier, Stoke City became the first team relegated from the Premier League following a 2-1 defeat to Crystal Palace at the bet365 Stadium.
Although Xherdan Shaqiri scored the opening goal from a free kick just before half-time, James McArthur equalised in the 68th minute and Patrick van Aanholt had Palace celebrating in the 86th.
Stoke, who entered second from bottom on 30 points, have not won since Paul Lambert's first game in charge on Jan. 20 -- a run of 12 games. A victory would have given them a chance at survival going into their final game, at Swansea City, next weekend.
They have not played in the Championship since the 2007-08 season, when they finished second to earn automatic promotion.
Palace, who guaranteed survival despite opening the season with seven consecutive league losses, are unbeaten over their last five games.