The quadruple-chasing Premier League leaders had looked like they would have to settle for a draw at the Etihad Stadium when Marco Reus levelled for the German side six minutes from time at the Etihad Stadium.
But Foden, who had twice tested Dortmund keeper Marwin Hitz in the second half of a controversial encounter, hit back from close range as the clock ran down.
Having taken the lead through Kevin De Bruyne, City now have the edge heading into next week’s second leg in Germany.
But, having failed at the last-eight stage in the last three seasons, Pep Guardiola’s side will be well aware they still have work to do.
Dortmund will also leave Manchester with reason to feel aggrieved after having a Jude Bellingham goal controversially disallowed before half-time.
Liverpool the side City look set to replace as English champions, will have to produce another knockout stage comeback against Spanish giants after a chaotic and ill-disciplined display saw them lose 3-1 to Real Madrid.
Jurgen Klopp’s team famously came from 3-0 down to beat Barcelona in the semi-final on their way to winning a sixth European Cup two years ago and the task in the last-eight second leg at home is likely to be just as difficult.
With no fans inside Anfield to produce that special European atmosphere and a team performing at a significantly lower level than in 2019, even an away goal given to them by Mohamed Salah’s 26th in 44 Champions League matches may not be of much help.
Talk of revenge for their 2018 final defeat to Real had been banished pre-match but in truth they hardly came close to laying a glove on the 13-time champions, for whom Vinicius Junior scored twice either side of one from Marco Asensio.
Liverpool’s side had five survivors from that meeting in Kiev three years ago – Andy Robertson, Trent Alexander-Arnold, Georginio Wijnaldum, Sadio Mane and Mohamed Salah – while Madrid had four.
Wijnaldum cut a frustrated figure, saying: “We were not concentrated enough, not sharp enough, It was difficult, I think because we played against a good side.”
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