On a night of fluctuating fortunes and thrilling football, Pep Guardiola's side were on the precipice in this tournament before dragging themselves back to ensure they go into the return in Monaco with a priceless lead.
Raheem Sterling gave Manchester City a 26th-minute advantage after fine work by Leroy Sane but Monaco proved their threat to lead before half-time through Radamel Falcao's header and Kylian Mbappe's powerful rising drive.
Falcao then saw a penalty saved by Willy Caballero just after the break before Monaco keeper Danijel Subasic's blunder gave Sergio Aguero his first goal.
Colombian Falcao, back to his best after failed loan spells at Manchester United and Chelsea, then lifted a brilliant chip over Caballero to put Monaco back in front - but this was the signal for City to launch an enthralling attacking salvo.
Aguero - who felt he was denied a first-half penalty after he tumbled under a challenge from Subasic - volleyed in another equaliser before John Stones made amends for poor defending in the build-up to Falcao's second by putting City ahead on the night with a sliding finish at the far post after 77 minutes.
Man of the match Sane handed City that two-goal cushion with a simple tap-in from Aguero's pass eight minutes from time - but Monaco's vibrant attacking ambition means this tie is far from over.
Source: Radio Television Brunei