Cassidy measured his race to perfection from P10 on the grid as the 22-strong field jostled for superiority over the 32-lap encounter, where Formula E's unique balancing act between energy efficiency and outright pace came to the fore.
The strategic battle for top spot was evidenced from the opening lap at Formula E's fourth US venue, as positions and race leaders changed corner by corner in groups five and six wide at points.
The Kiwi headed the way several times but finally got the better of da Costa, himself a race leader, on Lap 28 with the decisive move - only a few turns after the Portuguese had seized the initiative.
Cassidy first hit the front on Lap 3 while da Costa clambered through the pack from eighth at the outset to pile the pressure on the Envision Racing driver right to the flag but Cassidy held fast for a third win of 2022/23.
Polesitter Jake Dennis led the opening stages but wouldn't time his late-race charge as precisely as Cassidy managed to.
The Avalanche Andretti driver would settle for second, though, as that proved to be enough for the Drivers' World Championship lead as things stand - the Brit heading Cassidy by just a point and both taking full advantage with prior standings leader Pascal Werhlein (TAG Heuer Porsche) escaping contact to come home only ninth and in the points at the chequered flag. Third, meanwhile, was da Costa's first podium in seven rounds - the last being that win in Cape Town.
On his 29th birthday, Mitch Evans (Jaguar TCS Racing) recovered from 20th on the grid to fourth - ensuring he's still well in the fight for the title with four races to come in Season 9; two each at Rome next up on July 15 & 16 prior to the double-header finale in London.
As it happened...
Dennis flew away from pole as the pack filtered through the first chicane, with Sacha Fenestraz (Nissan) in tow while the big climber over the opening couple of laps was the NIO 333 of Dan Ticktum - the Brit up eight places to seventh by Lap 3.
The strategic battle began to play out immediately, with drivers unwilling to head the way and lifting early into the big stops - energy was predicted to be a priority for the teams on the ultra-quick, sweeping circuit.
The order in the opening stages would hardly be representative of the final shakeup but strong progress from 10th on the grid for Cassidy saw the second-placed driver in the standings briefly lead on Lap 3 before he became the first driver to jump for two of eight mandatory minutes' ATTACK MODE. A brief break in racing action followed a lap later with Roberto Mehri's Mahindra stranded on-track after suffering technical trouble and requiring recovery.
During the Safety Car we saw Fenestraz pit to replace his broken nose cone - heartbreaking for the front-row starter but it was his error; the French-Argentine running into the back of Dennis' Andretti. Back under racing conditions on Lap 8 and the lead group went for their first 50kW boosts - Cassidy taking his second early and Mortara holding off entirely.
On Lap 9, Nato was the incumbent leader, with da Costa, Guenther, di Grassi, Cassidy, Mortara, Dennis, Rast, Ticktum and Hughes the top 10 - though this order was changing several times over a given lap.
Lap 10 saw a big shunt for Nico Mueller in the ABT CUPRA who fired off the track at high speed into a 27G impact with the wall at Turn 10, reporting "no more brakes" though contact couldn't be ruled out.
Safety Car number two ensued. Just prior to the neutralisation, Cassidy retook the lead and pole position in the title fight - but this would by no means be the last word on the race order.
After a long delay we had the restart on Lap 17 with Nato leading Cassidy, Guenther, Mortara, da Costa, Dennis, Rast, di Grassi, Ticktum and standings leader Wehrlein rounding out the top 10.
The leader and the Maserati pair jumped for ATTACK MODE immediately, along with Rast - for their second boosts. Cassidy retook the lead from da Costa and Nato with the whole pack split by only three seconds.
The peloton caught out Wehrlein into Turn 1 on Lap 18 - the Porsche's front wing damaged and the German relegated down the order to 16th.
Six wide into Turn 1 on Lap 20 with drivers jostling for position and reluctant to be the first to make the jump and seize the initiative though Cassidy still held P1 - as he did in Berlin on the way to his race two victory - with Jakarta race two winner Guenther just behind. At the start of Lap 22, Porsche's da Costa made the jump on the leaders to hit the front as the field.
From there, the Season 6 champion began to stretch his legs and dictate the pace - drawing out just under a second on Cassidy in P2.
Four laps would be added on for those lost under the Safety Car. It was da Costa from Cassidy, Dennis, Guenther, Bird, Mortara, Vergne, Evans and Wehrlein.
On Lap 26, Cassidy once again jumped to the head of the pack into Turn 1. Track position was becoming king and Cassidy was defending hard as da Costa and Dennis behind looked for an opening. The latter made a nice move stick on da Costa through the first sector for second but he couldn't hold the Portuguese back for long as the pair swapped positions again half way around the same tour.
Da Costa then set about Cassidy - and made it by the leader on Lap 28 with a surprise leap into Turn 11. It wouldn't last any more than a few seconds, though, as Cassidy forced his way by once again into Turn 1.
On the final lap, da Costa held fast under severe pressure from Dennis - the Andretti man made it count to pinch second spot at the last from the Porsche driver.