The Kiwi had started ninth after missing out on the qualifying duels but stormed to the front of the pack just after the halfway point of the 29-lap race.
The race-winning move came into Sainte Devote on lap 18 as he overtook Mitch Evans, the Jaguar driver having jumped Cassidy at the same spot two laps earlier.
The race essentially became a five-lap shootout as the safety car was deployed after Maximilian Gunther’s Maserati MSG came to a stop heading into Massenet.
The German suffered damage on the run up Beau Rivage, having tried to overtake Dan Ticktum’s NIO 333 machine which had a damaged front-wing.
With energy saved behind the safety car and no added laps, the remaining tours were flat-out with Evans unable to find a way back past.
He was denied the chance of a last-lap overtake as a collision between Evans’ team-mate Sam Bird and Nico Muller left the Abt driver in the barrier at Sainte Devote.
The stranded car meant a second safety car as the race finished under caution, with Cassidy following on from his win in Berlin last month with his first success in Monte Carlo.
Source: Autosport