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.
Aguero's Manchester City future has been the subject of debate with recent arrival Gabriel Jesus appearing to find greater favour with manager Guardiola - but how can they seriously consider life without this world-class striker?
City may have been rattling at the back but Aguero was in magnificent form throughout, terrorising Monaco with his prodigious work-rate and sheer menace.
Aguero was denied a penalty in the first half when he was booked for diving after he was upended by Monaco keeper Subasic but he was not to be denied and was a key component of City's enthralling fightback.
He enjoyed some deserved good fortune when his shot went straight through Subasic for his first goal but he delivered a sumptuous right-foot volley to make it 3-3 and then set up Sane for the crucial fifth goal that gave City that two-goal advantage.
Aguero was substituted to a standing ovation and a kiss on top of the head from his manager with four minutes left - this was the night he delivered proof, as if it were needed, that he is the man City and Guardiola cannot do without.