The Jaguar driver was already top of the times with a lap that would have been good enough to end the session fastest heading into the final five minutes.
But the Kiwi, who won both races in Rome last year, set a blistering final lap as he became the only driver to go below the 1m38s barrier, setting a 1m37.881s, which was 0.613 seconds faster than championship leader Jake Dennis.
The Andretti Autosport driver was unable to improve on his final effort after suffering a small spin so remain second, while the Porsches of Antonio Felix da Costa and Pascal Wehrlein set late laps to move into third and fourth respectively.
Nick Cassidy was the first driver to go below the 1m40s barrier on Saturday morning, posting a 1m39.729s after the opening 10 minutes of the session as his Envision Racing team-mate Sebastien Buemi slotted into second.
Approaching the halfway point of the 30-minute session, Evans topped the standings for the first time with a 1m39.545s, which was surpassed just moments later by Rene Rast as the second McLaren of Jake Hughes moved up to third.
Buemi became the first driver to set a sub-1m39s lap with a 1m38.904s with 15 minutes still on the clock, leaving him 0.424s clear of Rast.
Times continued to tumble in the second part of the session, with Wehrlein and then Evans moving to the top of the leaderboard before the final attempts.
Behind the top four, Maserati’s Edoardo Mortara and Andretti’s Andre Lotterer completed the top six.
After setting the early pace, Cassidy - who sits just one point behind Dennis in the standings - slipped back to 15th at the chequered flag, 1.337s slower than Evans.
Wehrlein topped Friday afternoon’s much hotter FP1 session in the final moments with a 1m39.632s, while Jaguar’s Sam Bird slotted into second with his final lap placing him a further 0.272s behind.
Mortara completed the top three having initially topped the session for the final minutes, but he was just unable to break the sub 1m40s barrier by 0.004s as Buemi finished fourth.
Evans’ best time landed him fifth, but the Jaguar driver was unable to improve on his final run after being held up by the Mahindra of Roberto Mehri, the Kiwi pulling alongside and gesticulating towards the Spanish driver before confronting him in the pitlane afterwards.
Jean-Eric Vergne, who was handed a suspended fine by the FIA ahead of the meeting for comments made in the press, completed the top six for DS Penske.
Dennis endured a frustrating session as a broken suspension upright limited the Andretti driver to only a handful of laps at the end, which left him 18th on a 1m41.410s.
Both Abt Cupra drivers of Robin Frijns and Nico Muller were unable to register any timed laps after suffering with software issues.
Drugovich tops rookie session
Reigning Formula 2 champion Felipe Drugovich topped the rookie session, which was held ahead of FP1 on Friday afternoon, for Maserati.
The Aston Martin and McLaren F1 reserve driver posted a 1m43.736s that put him 0.312s clear of Sheldon van der Linde at the end of the 30-minute session.
Like Drugovich and the majority of drivers during the session, van der Linde was back behind the wheel of the Gen3 machine having also taken part in the Berlin rookie test earlier this season for Jaguar.
Luca Ghiotto (Nissan) and Charlie Eastwood (McLaren) completed the top four, as two-time World Touring Car Cup champion Yann Ehrlacher finished fifth for DS Penske on his first official on-track experience of Formula E.
Zane Maloney (Andretti), Yifei Ye (Porsche), Jack Aitken (Envision) and Daniil Kvyat (NIO 333) completed the timed runners.
Jehan Daruvala and Adrien Tambay were unable to set times for Mahindra and Abt Cupra respectively due to software issues.
FP2 result:
FP1 result:
