Substitute Divock Origi's 86th minute header earned Liverpool a 3-2 win at Newcastle United on Saturday to send them two points above Manchester City and keep their Premier League title bid alive.
The race to secure the final two Champions League qualification places looks likely to go to the final weekend after Tottenham Hotspur again slipped up, losing to a last-minute goal at Bournemouth while having two men sent off.
Cardiff City's 3-2 defeat at home to Crystal Palace ensured they were relegated along with Huddersfield Town and Fulham, who lost 1-0 at Wolverhampton Wanderers, while West Ham United brushed aside Southampton 3-0.
Liverpool have 94 points and Manchester City 92 but Pep Guardiola's City have two games remaining, including Monday's home match with Leicester City.
Liverpool have just their final day home game with Wolves remaining but the result means the race will go down to the wire.
Virgil Van Dijk headed Liverpool in front in the 13th minute, but seven minutes later Newcastle drew level through Christian Atsu.
Liverpool restored their lead in the 28th minute when Daniel Sturridge, starting in place of the injured Roberto Firmino, back-heeled the ball from the corner to Trent Alexander-Arnold and the full-back's cross was expertly turned in by Mohamed Salah.
Managed by former Liverpool boss Rafe Benitez, 14th placed Newcastle drew level nine minutes after the break when the visitors failed to clear a corner and Salomon Rondon's brilliant fierce left foot drive beat the helpless Alisson Becker.
Then, with their talismanic forward Salah carried off on a stretcher with a head injury and facing a massive blow to their title hopes, Origi rose at the near post to head in a Xherdan Shaqiri free-kick and give Juergen Klopp's side the victory.
A win for Spurs at the Vitality Stadium would have secured a top-four slot ahead of next week's Champions League semi-final second leg against Ajax Amsterdam.
But, after losing at home to West Ham United last week and then going down to the Dutch side in midweek, Mauricio Pochettino's side failed to fire again and went down 1-0 after Nathan Ake struck in injury time.
Son Heung-min was first to be sent off for pushing Jefferson Lerma just before halftime with Juan Foyth shown a straight red card for a studs-up tackle on Jack Simpson two minutes after coming on at the interval.
Spurs stay third on 70 points, four points clear of fifth-placed Arsenal, who have two games remaining. But Pochettino's side know victory in their final game against Everton will see them qualify, with Chelsea and Manchester United also capable of securing a top-four slot.
"It is very painful to play with two players less than the opponent," Pochettino said.
"We need to move on. We cannot change the decisions. We have ahead two finals against Ajax and Everton. It is in our hands. If it does not happen we will be proud because nobody expected Tottenham to be in the position they are today.
"We are fighting (five) teams, it is impossible for all six to get the top four, whatever happens I will feel proud and whatever happens in the (Champions League) semi-final I will be proud."
Spurs also had to contest with a fine Premier League debut from 19-year-old goalkeeper Mark Travers, who was in inspired form for the hosts with a string of fine saves.
Cardiff never seriously looked like securing the win they needed to stand any chance of staying up, with Wilfried Zaha, Michy Batshuayi and Andros Townsend scoring the goals for Palace, who won for the fifth time in six away league games.
The result confirmed Cardiff's relegation after one season for the second time in five years. It was also manager Neil Warnock's third top-flight relegation after also going down with Notts County in 1992 and Sheffield United in 2007.
At Molineux, Leander Dendoncker's 75th-minute volley against Fulham moved Wolves a step closer to possible European football next season.
The Midlanders will be guaranteed to finish seventh in their first season after promotion if Leicester fail to beat Manchester City on Monday. Wolves would then need City to beat Watford in the FA Cup final to secure a place in Europe for the first time in 39 years.
The one bright spot for Fulham was Harvey Elliott, who became Premier League's youngest ever player at the age of 16 years and 30 days when he came on after 88 minutes.
Marko Arnautovic scored twice for West Ham - his first goals for four months - as the home side completed a routine 3-0 win over Southampton. Ryan Fredericks rounded off the scoring with his first-ever Premier League strike.