Alexis Sanchez sank Sunderland to keep Arsenal in the hunt for Champions League qualification on Tuesday, while Manchester City all but secured a top-four place by beating West Bromwich Albion. Sanchez scored two late close-range goals to earn Arsenal a 2-0 home victory over relegated Sunderland, while Kevin De Bruyne starred as City comfortably defeated West Brom 3-1 at the Etihad Stadium. City climb to third in the Premier League, two points above Liverpool and three points clear of Arsenal, with only the teams finishing third and fourth assured to join Chelsea and Tottenham Hotspur in the Champions League.
"We've got in on the final day many times," Arsenal manager Arsene Wenger told BBC Sport at the Emirates Stadium.
"We made 71 points and were second. We now have 72 and want to go to 75. After that you deal with what happens."
Arsenal must win their final game at home to Everton on Sunday and hope Liverpool slip up at home to relegated Middlesbrough if they are to guarantee a 20th successive season of Champions League football.
As well as their points advantage over Arsenal, Jurgen Klopp's Liverpool also have a superior goal difference (+33 to +31).
A point at Watford on Sunday will guarantee a top-four place for Pep Guardiola's City, but they can secure third place -- and, crucially, avoid the Champions League play-off round -- if they win.
"Now we are in third and it's in our hands to finish third," said City manager Guardiola.
"We're going to travel to Watford to win and to finish third."
A conspicuous number of empty seats at the Emirates Stadium articulated the apathy that has taken hold among Arsenal fans this season and Wenger's team made heavy work of beating Sunderland.
They had the best of the first half, with Hector Bellerin striking the outside of the post from one of a succession of home attacks.
But rock-bottom Sunderland twice threatened on the counter-attack, with Arsenal goalkeeper Petr Cech obliged to save from Didier Ndong and Jermain Defoe.
- Zabaleta farewell -
Sunderland goalkeeper Jordan Pickford looked set to foil Arsenal in the second half, saving from Aaron Ramsey and substitute Danny Welbeck, but in the 72nd minute the hosts' pressure told.
Granit Xhaka's lofted pass was squared by Mesut Ozil and Sanchez volleyed in his 22nd goal of the league campaign from beneath the crossbar.
After Pickford had thwarted Sanchez, Xhaka and Alex Iwobi, Sanchez made sure of the points in the 81st minute, heading in after Pickford had blocked Olivier Giroud's volley.
Guardiola is now within touching distance of securing his minimum objective of Champions League qualification following a straightforward home win over West Brom.
After Aleksandar Kolarov's free-kick was pushed behind by visiting goalkeeper Ben Foster and Leroy Sane had dragged wide, City went ahead in the 27th minute with a fine team goal.
Sergio Aguero's artful back-heel released De Bruyne, whose deflected cross from the left was tapped in by Gabriel Jesus.
De Bruyne doubled City's lead within two minutes when he shaped a half-volley inside the right-hand post from the edge of the box.
Yaya Toure added a third shortly before the hour, exchanging passes with Aguero, driving into the box and slotting home.
Guardiola used the final half hour to offer Pablo Zabaleta a farewell appearance in City's colours.
The popular Argentine right-back, who has been at the Etihad for nine years, is due to leave the club at the end of the season.
"My favourite moments were when we beat Manchester United in the (FA Cup) semi-final at Wembley (in 2011) and the first Premier League we won with Sergio Aguero's goal (in 2012)," Zabaleta told fans in an on-pitch address.
"The fans had waited so long and we did it in a City way."
Substitute Hal-Robson Kanu claimed a consolation goal for West Brom with three minutes remaining.