City and Leeds both claimed important points on the penultimate weekend of the season.
Mas Jack Grealish pulled one back shortly after half-time and Vladimir Coufal headed into his own net in the 69th minute to draw City level.
City had a golden chance to win it when they were awarded a late penalty but Lukasz Fabianski saved Riyad Mahrez’s effort.
Pascal Struijk came off the bench to earn Leeds a potentially vital point in a 1-1 draw with Brighton.
Danny Welbeck put the visitors ahead in the 21st minute but Leeds’ second-half efforts paid off in injury time when Struijk conjured an equaliser to lift the Whites out of the relegation zone.
They have been replaced in the bottom three by Burnley, who have a game in hand but are now one point behind their rivals after a 1-0 defeat by Tottenham.
Harry Kane scored the only goal from the penalty spot in first-half added time after referee Kevin Friend ruled that the ball flicked Ashley Barnes’ outstretched arm following a VAR check.
Barnes hit a post in the second half but Nick Pope produced a string of saves in the Burnley goal as Spurs piled the pressure on Arsenal in the battle for Champions League qualification.
Jamie Vardy and Harvey Barnes each scored twice as Roy Hodgson’s final home match in charge of relegated Watford ended in an embarrassing 5-1 loss to Leicester.
Joao Pedro’s deflected effort gave the Hornets an early lead in front of incoming head coach Rob Edwards.
But familiar defensive issues contributed to the hosts’ downfall as James Maddison’s leveller and doubles from Vardy and Barnes condemned them to a 26th Premier League loss of a miserable campaign.
Substitute Jeffrey Schlupp netted a late equaliser as Crystal Palace secured a 1-1 draw at fellow mid-table side Aston Villa.
Schlupp finished from close range in the 82nd minute to cancel out Ollie Watkins’ 69th-minute opener.
Rayan Ait-Nouri’s first goal in 19 months salvaged a point for Wolves against relegated Norwich.
The defender struck to rescue a 1-1 draw at Molineux after Teemu Pukki’s 11th goal of the season gave the Canaries a first-half lead.