The Portuguese had surged from 11th on the grid to factor into the leading battle, taking the lead from Nick Cassidy on the 24th lap with a brave outside pass in the flat-out Turn 8 before motoring off into the distance.
With enough of a lead to take his second and final attack mode, da Costa missed one of the three activation loops and haemorrhaged part of his lead to the chasing Vergne, still with a minute of 350kW left to take.
Two laps later, da Costa went again and this time came up for air with attack mode successfully triggered, but Vergne swept into the lead in his bid to win a second race on the bounce.
The Porsche driver did not give up the fight, looming large in Vergne's mirrors over the final laps and using the slipstream to get level on energy with his former DS Techeetah team-mate.
On the first of the two added laps, da Costa managed to complete a carbon copy of his move on Cassidy and swept into the lead to enthral the sell-out Cape Town crowd.
It was a matter of closing out the race from there and, once da Costa had warded off Vergne at Turn 10 at the end of the beachfront stretch, the 2019-20 champion could cross the line for a famous victory.
Da Costa and Vergne had moved up into the top three following Maximilian Guenther's lap 21 crash as he hit the wall at Turn 1. As the Maserati MSG driver pulled up to stop, a full-course yellow period was introduced just as the leading pair of Cassidy and Sacha Fenestraz collected attack mode.
While Cassidy held on, Fenestraz lost positions to da Costa and Vergne at the introduction of the short yellow-flag period while Guenther's car was cleared from the Turn 4/5 chicane run-off.
This opened the door for da Costa to continue his compelling charge through the field, with Cassidy falling to his gutsy move.
Vergne was effusive in his praise of da Costa's move, and had to be content with second despite his attempts to find a way past on the final lap.
Cassidy completed the podium after leading most of the final two-thirds of the race, and although the New Zealander fell behind polesitter Sacha Fenestraz, the Franco-Argentine driver crashed on the final lap to allow Cassidy to claim a second podium on the bounce.
Envision driver Cassidy had battled side-by-side with Guenther at the start for second, but relinquished his grip on the position to ensure he could benefit from the slipstream from the drivers ahead.
An early safety car, brought out on lap 2 as championship leader Pascal Wehrlein locked up into Turn 10 and speared into the back of Sebastien Buemi, caused confusion among the front-runners as Guenther picked up the lead from Fenestraz as they slowed for the initial full-course yellow.
Guenther did not cede position to Fenestraz, earning an investigation for his efforts, and the Nissan driver then fell behind Cassidy during this initial foray into the attack mode zone.
Cassidy then grabbed the lead from Guenther as the Maserati MSG driver bagged his first attack mode, and the Kiwi managed to break-build to ensure he could retain the lead after his first attack mode.
But leading the race on the flat-out Cape Town course meant that the Jaguar-powered car was consuming more energy - and Cassidy also reckoned that the full-course yellow cost him a shot at victory.
Rene Rast picked up fourth place after Fenestraz's late crash, while Buemi shook off the earlier Wehrlein contact to claim fifth place.
Dan Ticktum wrapped up sixth place in another impressive race for NIO 333, as Stoffel Vandoorne claimed seventh after Andre Lotterer was handed a five-second penalty for a safety car infringement.
Norman Nato collected a conciliatory eighth for Nissan ahead of Lotterer, as Jake Hughes completed the top 10.
Mitch Evans placed 11th despite an earlier drive-through penalty for an overpower spike, with Sergio Sette Camara ahead of Jake Dennis - who also faced a drive-through for a minimum tyre pressure infraction.
The Mahindras of Lucas di Grassi and Oliver Rowland, along with the Mahindra-powered Abt cars of Kelvin van der Linde and Nico Muller, withdrew ahead of qualifying owing to safety concerns with its rear suspension package.
Sam Bird was also unable to start as his Jaguar could not be fixed in time following his hefty qualifying crash at Turn 9.
Cape Town E-Prix Results:
| Cla | Driver | Team | Laps | Gap |
|---|---|---|---|---|
| 1 |  Antonio Felix da Costa |
 Porsche Team |
32 | |
| 2 |  Jean-Eric Vergne |
 Dragon Racing |
32 | 0.281 |
| 3 |  Nick Cassidy |
 Virgin Racing |
32 | 1.808 |
| 4 | René Rast |
McLaren |
32 | 2.208 |
| 5 |  Sébastien Buemi |
Virgin Racing |
32 | 2.656 |
| 6 | Dan Ticktum |
NIO Formula E Team |
32 | 3.209 |
| 7 |  Stoffel Vandoorne |
Dragon Racing |
32 | 4.210 |
| 8 | Norman Nato |
 Nissan e.Dams |
32 | 8.582 |
| 9 | Andre Lotterer |
Andretti Autosport |
32 | 8.755 |
| 10 | Jake Hughes |
McLaren |
32 | 10.475 |
| 11 | Mitch Evans |
Jaguar Racing |
32 | 14.183 |
| 12 |  Sergio Sette Camara |
NIO Formula E Team |
32 | 14.914 |
| 13 | Jake Dennis |
Andretti Autosport |
32 | 38.846 |
| 14 | Sacha Fenestraz |
Nissan e.Dams |
32 | 47.613 |
| Maximilian Gunther |
 Maserati Racing |
20 | 12 Laps | |
| Edoardo Mortara |
Maserati Racing |
1 | 31 Laps | |
| Pascal Wehrlein |
Porsche Team |
0 | ||
| View full results | ||||
