Evans' British teammate Sam Bird (36) was third with fastest lap in the Sao Paulo E-Prix, making a first podium sweep for the Jaguar powertrain that is also used by Envision.
Porsche's Pascal Wehrlein (28) retained the overall lead in the all-electric city-based championship after starting 18th on the grid and finishing seventh in the sixth round of the season.
Wehrlein now has 86 points to 62 for Andretti's British driver Jake Dennis (27), who failed to score for the third race in a row - this time after contact from compatriot Dan Ticktum's NIO pushed him into Wehrlein.
Cassidy moved up to third overall and on 61 points after finishing on the podium three races in a row for the first time in his Formula E career.
Evans's first victory of the season made him the fifth different winner in six races of the series' new Gen3 era, with no driver so far able to convert pole position to victory.
"This has come at the perfect time. We had a tough start but the car has been quick, so to finally get the victory and some points is incredible," said Evans, who took the lead from his compatriot on lap 32.
The top three finished only half a second apart, Evans beating Cassidy by 0.284 seconds, on the 11-turn track in a race with two safety car periods and plenty of incidents.
Porsche's Antonio Felix da Costa (31) was fourth with DS Penske's Jean-Eric Vergne (32) fifth.
DS Penske's defending champion Stoffel Vandoorne (30) started on pole but the Belgian ended up sixth, with McLaren's Jake Hughes (28) and Rene Rast (36) eighth and ninth and Sebastien Buemi (34) taking the final point for Envision.
The championship now moves to Berlin for two races on April 22nd and 23rd.
