City had looked on course to come back and win the tie behind closed doors at the Estadio Jose Alvalade after Kevin De Bruyne's goal midway through the second half had cancelled out Maxwel Cornet's first-half opener.
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However, Dembele put Lyon back ahead in the 79th minute and then capitalised on a shocking miss by Raheem Sterling to clinch the victory three minutes from the end.
Against all expectations, a team who finished seventh in the curtailed French season, and had played just two competitive games since early March, now find themselves through to a Champions League semifinal on Wednesday against Bayern Munich.
That, surely, will be a step too far for Rudi Garcia's team but then again nobody expected them to eliminate Juventus in the last round, never mind knock out City here.
"We are still in it, which means we have a great team," former Celtic striker Dembele told French television channel RMC Sport.
"We are taking it game by game, not getting carried away. We will try to be ready for Bayern."
Guardiola's team had been warned about Lyon, losing at home and then drawing away against the French club in last season's Champions League.
But that was almost two years ago now and Lyon had lost several key players since then.
This, a day after Bayern's 8-2 demolition of Barcelona, is a seismic shock and a hammer blow to the ambitions of City under Guardiola.
Their wait for European glory will go on, with this a third consecutive quarterfinal exit.
"It is what it is. Maybe one day we are going to break through the quarterfinals. We are not able to do it now, with these incredible guys, but we are going to try in the future," Guardiola said.
He was brought to the Etihad Stadium to deliver the Champions League, but he has not managed to equal the club's best performance to date in the competition, a semifinal appearance in 2016, just before he was appointed.
