Teenager Eliesse Ben Seghir capped a very fine performance with the opener midway through the second half, before Lamine Camara struck to secure the three points for the away side.
Lyon have had another difficult beginning to their league campaign and, after going down 3-0 at Rennes last weekend, have now shipped five goals in the opening two matches after being the form side of Ligue 1 in 2024.
"It's incredible, we'd never won here," said Ben Seghir.
"We won by two goals, it's the third match where we've kept a clean sheet (including a friendly against Barcelona), that shows the way we play."
Things started poorly for the hosts when they were forced into an early change after forward Ernest Nuamah appeared to pull a muscle and was replaced by new-signing Georges Mikautadze.
The best chance of the first period fell to Monaco's Japanese attacker Takumi Minamino on the half-hour.
The ex-Liverpool man wriggled free of the defence inside the box with a deft touch but Lucas Perri flew out to narrow the angle and his outflung arm tipped the ball onto the far post.
Lyon looked to have come close to grabbing an unlikely lead right on the stroke of half-time but Philipp Koehn shot off his line quickly to nullify the danger, before a goal-kick was signalled as Said Benrahma had marginally overrun the ball in the build-up.
After the break Monaco continued to dominate with the tricky Ben Seghir continuing to cause problems for the Lyon defence.
The Moroccan found Minamino in a central position, who then laid the ball off to Breel Embolo but the forward's powerful drive from just outside the box flew over the crossbar.
Embolo then passed up another chance on 63 minutes when Maghnes Akliouche lofted a cross into the box and he attempted an overhead kick inside a crowded box, which blazed over the goal.
But Monaco pressure soon told and inevitably it was Ben Seghir and Akliouche that caused the breakthrough on 65 minutes.
The 19-year-old zipped a pass into Akliouche, who then returned the favour before Ben Seghir shifted the ball onto his right foot in very little space and threaded a cute finish into the far corner.
Camara then put the match to bed as a contest in the 80th minute when he swept in unmarked at the back post to finish emphatically from Kassoum Ouattara's cross.
Lyon now looked very leggy and a sequence of errors gifted Akliouche a glorious chance with seven minutes remaining but ballooned his effort high and wide with just Perri to beat.
A dampener was put on Monaco's day at the very end, however, when Camara picked up a second yellow for a late challenge.
Later on Saturday, Lille host newly-promoted Angers and Saint-Etienne's Le Chaudron stadium sees the return of top-flight football after two years with the visit of Le Havre.
