Despite their stoppage-time defeat, Southampton still ended up celebrating Premier League survival with Swansea City, who lost 2-1 to Stoke City, going down while Tottenham Hotspur emerged victorious 5-4 from an incredible seesaw encounter against Leicester City.
On a day of farewells, with more than half the managers either departing or with questions about their future and several distinguished players ending their club careers, Arsenal boss Arsene Wenger signed off with a 1-0 win at Huddersfield.
Yet Chelsea's Antonio Conte, who is widely expected to leave after next week's FA Cup final, saw his side beaten 3-0 at Newcastle United. Manchester City's season looked to be heading for an equally underwhelming end after they failed to register a single first-half shot on target at St Mary's where Southampton knew they would be safe provided City did not run riot.
There was never much chance of that but City's thrilling season was capped by another piece of individual brilliance, with Gabriel Jesus producing a superb lobbed winner in the 94th minute to spark wild celebrations.
Aside from the new all-time English top flight points record, City have also set new benchmarks for Premier League goals (106), wins (32) and points clear of the second-placed team (19).
At Anfield, they were also scouring through the record books after Salah opened the scoring against Brighton and Hove Albion with his 32nd goal of the season.
That established a new mark for a 38-game campaign, beating the previous 31-goal record he shared with Alan Shearer, Cristiano Ronaldo and Luis Suarez.
Dejan Lovren added a second before Dominic Solanke and Andy Robertson registered their first goals for the club in the 4-0 win.
There was further good news for Liverpool and England in the form of a 20-minute cameo for Adam Lallana, who saw his first action since the end of March.
Harry Kane did his best to chase Salah all the way at the top of the Premier League goalscoring charts, netting twice in Spurs' amazing win over Leicester, a game they twice trailed in. The win confirmed Spurs finished third.
At the bottom of the table, Swansea took the lead against Stoke although their afternoon rapidly turned into a wake as their seven-year Premier League stay ended in what is expected to be Carlos Carvalhal's final game in charge.
Badou Ndiaye and Peter Crouch scored the goals for Stoke, who will join the Swans in the Championship next season.
Angel Rangel and Leon Britten both said their farewells after distinguished careers for Swansea and there was more emotion at Huddersfield where Arsenal manager Wenger signed off after overseeing his 1,235th game.
The home club presented the Frenchman with a special shirt in celebration and, thankfully, Pierre-Emerick Aubameyang scored to end Arsenal's woeful away run that had left them without a win all year.
Manchester United's Michael Carrick was another signing off at Old Trafford where the home side beat Watford 1-0 to consolidate their hold on second place.
Elsewhere, Everton and former West Ham manager Sam Allardyce, whose position is under threat, found himself booed by both sets of supporters as the Hammers rounded off their underwhelming season with a welcome 3-1 win.
Burnley lost 2-1 at home to Bournemouth, with Chris Wood scoring for Burnley, while West Bromwich Albion's season ended in a 2-0 defeat at Crystal Palace, a result that ensured they finished bottom of the league.
It was also caretaker manager Darren Moore's first defeat and will have not done much for his chances of ensuring he gets the job permanently.