Da Costa’s best lap – a 1m11.496s – came as the chequered flag was shown at the Brazilian venue after the Portuguese driver had not featured near the top of the times for the majority of the 30-minute session.
Gunther finished second having occupied the top of the times for a large portion of the running with a 1m11.762s, putting him 0.266s behind da Costa, while Nissan’s Norman Nato completed the top three.
After the opening 10 minutes Nick Cassidy’s 1m13.192s had been enough to occupy the top of the times for Envision, but this was soon surpassed by Stoffel Vandoorne – the DS Penske driver the first man to dip into the 1m12s with a 1m12.611s.
Cassidy's Envision team-mate Sebastien Buemi then moved to the top of the leaderboard by a fraction with a 1m12.554s, before Lucas di Grassi set a 1m12.203s just before the halfway point for Mahindra.
Buemi then lowered his best to a 1m12.073s, with Jaguar’s Sam Bird moving into second – just 0.061s in arrears with 13 minutes remaining.
Nato became the first man into the 1m11s, setting a time 0.310s faster than Buemi, but pushed too hard on a following lap and ran wide at the Turn 4 chicane.
With eight minutes remaining Gunther moved to the top of the times, just 0.001s better than Nato’s fastest effort, before both were surpassed by da Costa in the dying moments.
Da Costa’s Porsche team-mate and championship leader Pascal Wehrlein finished fourth with a 1m11.853s, while a late effort from Jake Dennis moved the Andretti Autosport driver up to fifth with a 1m11.872s.
Cassidy’s 1m11.921s ensured he completed the top six after heading the times early on, as just half a second covered the top 10 drivers.
Buemi had set the pace in Friday’s FP1 running, his 1m12.341s just over a tenth faster than Sacha Fenestraz.
Times tumbled in the final minutes as the track rubbered in and temperatures dropped, with Buemi setting his best lap five minutes from the end of the session.
Nissan’s Fenestraz shot up to second shortly after the chequered flag was shown, demoting NIO 333 driver Dan Ticktum down to third.
Reigning champion Vandoorne finished fourth, but was the first driver to find the barrier, running wide on the exit of Turn 1 and into the tyre wall before rejoining with damage to his front wing.
He wasn’t the only driver testing the limits at the opening corner, as several took to the run-off area including Wehrlein, who finished down in 12th on the times.
Formula E rookie Jake Hughes occupied the top of the times at several moments during the session, but slipped to seventh by the flag, just 0.238s off Buemi’s fastest time.
