Pep Guardiola's side were in command after Jack Grealish put them ahead in the first half and Rico Lewis doubled the lead after the break.
But the champions collapsed in the second half at the Etihad Stadium as Jean-Philippe Mateta reduced the deficit in the closing stages before Olise converted his penalty in the fifth minute of stoppage-time.
It was the fifth time in six league games that Pep Guardiola's men have dropped points, having also drawn with Chelsea, Liverpool and Tottenham and lost to Aston Villa prior to last Sunday's 2-1 win at Luton.
In what was their last match before heading to Saudi Arabia for the Club World Cup, the result leaves them fourth in the table, three points behind leaders Liverpool, who host Manchester United on Sunday.
City's bid for an unprecedented fourth successive title is in danger, although Guardiola will remind his players they came from eight points behind Arsenal to snatch the crown late last season.