Man City conceded within the first eight minutes of the game when hotshot striker Kylian Mbappe prodded home from close range.
Fabinho then hit home to turn the tie around, meaning City had to score.
That goal came as the game entered the final stretch, with Sane slamming home into the roof of the net.
But Bakayoko ensured that the Ligue 1 leaders would go through when he hit home 12 minutes from time.
Here are five things we learned:
1. Guardiola got his tactics wrong
For such an experienced and revered coach, Pep Guardiola got it spectacularly wrong last night, by trying to go toe-to-toe with Monaco, the highest scorers in Europe’e top divisions this season with 123 goals.
With only Fernandinho to offer protection to the Defence, City were left vulnerable and exposed, and paid a heavy price for their manager’s gamble, which ultimately backfired.
2. City’s defence in disarray
Given the free-scoring nature of the first-leg, it was unrealistic to think City could extend their run of six consecutive away clean sheets here.
3. De Bruyne wakes up after sloppy first-half
Kevin De Bruyne has been one of City’s most impressive players this season, not scoring as freely as last term, but showing greater influence in games.
Here, however, he endured a wretched first-half, before raising his game after the break, his fine ball to Raheem Sterling starting the move that led to City’s vital goal.
But at this level, with so much at stake, De Bruyne needed to produce more.
4. Aguero misses prove costly
Sergio Aguero has flourished since winning back his place after injury sidelined Gabriel Jesus, with six goals in his last five games, but here he spurned three glorious second-half chances to put City ahead on aggregate.
He was denied by a fine challenge from Andrea Raggi, shot over the bar and then saw Danijel Subasic block his shot after a one-on-one with the Monaco keeper.
5. Mbappe justifies the hype
On the eve of the game, Bacary Sagna likened Monaco’s 18-year-old forward Kylian Mbappe to former France and Arsenal striker Thierry Henry.
Here the teenager justified that high praise, tormenting City’s defence with his pace, quick movement and lethal finishing, as he showed by plundering the opener.