Cassidy started from ninth, with Evans sixth, and both drivers picked cars off one by one as their stronger race pace proved crucial around the Principality.
Jake Dennis took the final step of the podium but trails Cassidy by 25 points, while Pascal Wehrlein finished down in 11th.
“I’ve got nothing against Berlin but this feels special!” said Cassidy. “I’m lost. It’s gonna take a bit to sink in but we had such a tough day
“We were struggling a lot. I qualified 10th and was happy with that so that was the way our car was going.
“Mitch showed how bloody strong he is, so it’s going to be a great fight.”
It was a cagey start to the race as pole-sitter Jake Hughes led the opening opening laps from Sascha Fenestraz before taking his first attack mode and began to drop down the order.
Then, the action came when everyone decided to take their attack modes by the halfway point of the race with 14 laps remaining, so Cassidy, Evans and Dennis came to the fore.
Evans and Cassidy traded the leading positions as Dennis, who started 11th made his way up to third.
The slipstream effect didn’t seem to be as strong compared to Berlin and Sao Paulo, but the pack was still close together.
It all kicked off from Lap 20 when Da Costa had a problem on the run down to Tabac, then Dan Ticktum was involved in two incidents one lap later.
Ticktum hit the back of Fenestraz at the Rascasse, then was Maximilian Gunther ran into the back of him up the hill towards Bea Rivage. Gunther came to a halt which caused a safety car.
On the restart, with five laps to go, Cassidy led Evans, Dennis, Fenestraz, Hughes, a damaged Ticktum and Jean-Eric-Vergne, who slowly came from the field from the back of the grid after a tyre pressure infringement in qualifying.
No additional laps were set to be added on so it came to a flat out race and Cassidy did enough to not allow Evans to make a move.
Nico Muller crashed at Turn 1 with one-and-a-half laps remaining following contact with Sam Bird, so the race ended behind the safety car and Cassidy secured his second consecutive victory.
He leads Wehrlein by 21 points, with Dennis a further four points adrift and Evans another two points behind. Vergne‘s seventh place limited the damage but he is 34 points behind Cassidy.
There is a four-week break until the next Formula E rounds in Jakarta on June 3-4.