The hosts must have thought that another routine home win was imminent - but Basel had other ideas.
Mohamed Elyounoussi levelled the game less than 10 minutes after Jesus' opener, before Michael Lang swooped in the second half to send Basel home with a memorable win.
The Citizens nevertheless march into the quarter finals with a 5-2 aggregate win, but the loss ends an incredible run of form in front of their own fans since Pep took over.
City last lost a home match on December 3, 2016, when eventual Premier League champions Chelsea inflicted a 3-1 defeat.
Since that date Guardiola's men had gone no less than 36 matches without losing at the Etihad, a run that included 29 wins and seven draws.
The Premier League leaders will be back in action at home on April 7 against local rivals Manchester United - a match that could see City seal the Premier League title.