After running well during practice, Gasly qualified a lowly 17th after a strategy mix-up by AlphaTauri prevented him from setting a time at the end of Q1.
The Frenchman told his team to "be prepared" to take risks on strategy in the race, prompting him to be the first driver in the field to switch from wet to intermediate tyres after the red flag restart.
Gasly survived a couple of sketchy laps in the wet before conditions improved and he became the fastest driver on track, allowing him to quickly catch those still running on wets.
Gasly closed up on Ricciardo for 12th through the Nouvelle Chicane on lap 14, and had a quick look up the inside at Tabac before ducking back behind the McLaren.
But thanks to his superior grip, Gasly was able to pull alongside Ricciardo exiting the corner before then completing the move on the entry to Swimming Pool, which is rarely an overtaking spot in Monaco.
"It was pretty tight, but I was so much faster than these guys, I just needed to calm myself," Gasly explained after the race.
"I'd caught them so quickly, and then after you are like, OK, I want to pass, but it's like if the guy is defending well, suddenly you've got no space on the right, no space on the left.
"Then you have to be creative. That's what I tried to do. At the end of the day, F1 drivers, we are kind of artists, we need to find always new ideas.
"I tried to come up with unusual places to overtake, and that worked out, so I'm pleased with that."
Gasly admitted that he did not know "how many times I almost crashed" and that when he initially exited the pit lane on intermediate tyres, he thought it "might have been a very bad idea".
"But I needed it to work somehow," he said. "It's also an exercise I really like. It's a big challenge trying to find the grip, and I must say, today, driving-wise, was really good.
"Unfortunately, we just started too far and we paid the price for our bad choices in quali."
Gasly finished 12th on track and was classified 11th after Esteban Ocon's penalty was applied, leaving him one place shy of a points finish.
"I'm a bit sad not to be rewarded with a point at the end, because I felt like I probably deserved it," Gasly said.
"We lost quite a bit of time in our first pitstop, six or seven seconds, second pitstop, like around three seconds. There's 10 seconds of race time that we left that cost us probably a point.
"But in the end, there are a lot of positives to take from that weekend looking at free practice and the pace today, so that's what we remember."
