Frank Lampard scored for Manchester City in his final Premier League appearance as Southampton missed out on a top-six finish.
Ronald Koeman’s men must now hope Arsenal can defeat Aston Villa in next weekend’s FA Cup final to help them earn a place in next season’s Europa League.
Lampard, who is set to play for New York City FC in the USA, side-footed home from 10 yards to give the hosts a first-half lead.
Sergio Aguero doubled that advantage with a close-range header into an empty net, having seen three earlier efforts saved by Kelvin Davis.
Victory for City saw them consolidate second place in the table, ending the season eight points behind champions Chelsea.
For Southampton, 60 points still marks their highest total in the Premier League and they must now wait a week to find out whether seventh will be enough to seal European football.
City’s statistical success
Despite finishing eight points behind title winners Chelsea, Manchester City finished the season with the most goals, the individual top scorer, the best goal difference and the most clean sheets.
Tottenham and Liverpool have already secured a Europa League place by finishing above Saints, but the qualifying spot handed to the FA Cup winners will go to Southampton, if Champions League-bound Arsenal lift the trophy at Wembley.
As well as Lampard’s final game for City, both goalkeepers Joe Hart and Davis were making their 300th appearances for their respective clubs.
And other than Hart’s low save from Shane Long, Davis was kept the busiest with a point-blank save from Aguero and two further stops to deny the Argentine in the first half.
The goal came from good work by James Milner on the right to tee up Lampard who arrived late in the box to fire home from 10 yards.
It was Lampard’s 177th goal in the Premier League and the midfielder almost added to that total with a back-post header which Davis kept out. At the other end Long had a low strike from 18 yards comfortably saved by Hart.
Sadio Mane, who scored a three-minute hat-trick last weekend, had Southampton’s best chance of the second half but he mistimed his header and failed to trouble Hart.
Lampard, who delivered a speech to the crowd and was held aloft in celebration by his team-mates after the final whistle, was replaced after 75 minutes and received a standing ovation from the home fans.
And the supporters were on their feet again with five minutes left as Aguero headed home his 26th Premier League goal at the back post from two yards out to seal victory.