Vergne logged his headline time immediately after the chequered flag fluttered over the finish line, jumping above Mortara to take the early bragging rights ahead of the second day of running at the Circuito Cittadino dell'EUR.
On a brisk morning, with vigorous winds breathing eight-degree air around the circuit, race 1 winner Mitch Evans kicked off the post-installation running with a lap in the 1m43s.
The times quickly began to wind down, with Saturday's runner-up Robin Frijns posting a 1m41.788s lap before a red flag curtailed the early set of runs as Oliver Askew pulled over following the Turn 12-13 chicane, parking his Andretti in the bus lane with an unspecified mechanical issue.
After a four-and-a-half minute pause in proceedings, Antonio Felix da Costa made hay under the returning green flag conditions and leaped to the top with a 1m41.766s lap, but that was immediately crushed by Mahindra's Oliver Rowland, who fired in a 1m40.108s lap on the full 250kW power mode.
Frijns took his own maximum power lap afterwards, diving 0.3s below Rowland's benchmark to collect a 1m39.885s laptime.
He looked set to be challenged by Mortara taking his first 250kW lap, but the Swiss driver was off-line trying to pass a slow Sam Bird ahead of the chicane - and scraped the wall before going too deep into the corner, eradicating any advantage.
Da Costa returned to the top with a 1m39.662s, although an expected assault from the Mercedes duo of Stoffel Vandoorne and Nyck de Vries was put on ice when Antonio Giovinazzi came to a brief stop at Turn 8, requiring a double-yellow flag before the home favourite got up and running again.
Jake Dennis then hammered in a 1m39.565s to go to the top for a brief spell, before Mortara returned to assert his credentials with a 1m38.866s, almost three quarters of a second quicker than the Andretti driver.
Mortara then saw off a sea of challenges; Frijns was unable to break into the 1m38s before being displaced from second by Dan Ticktum, who hustled his NIO 333 machinery into delivering a 1m39.257s lap.
But with the session due to end, Vergne collected a 1m38.608s time to move to the top, as Mortara's time remained good enough for the runner-up spot.
Bird's lap late on was good enough for third as Ticktum impressed with his run to fourth overall, keeping a late run from Pascal Wehrlein at bay as the Porsche driver was fifth in the timesheets.
Wehrlein's teammate Andre Lotterer was sixth fastest ahead of Evans, as da Costa, Frijns and Lucas di Grassi completed the top 10.
The session ended with a late stoppage for Dragon Penske's Sergio Sette Camara, who yesterday felt he should have been on for a duels performance before encountering a slow Nick Cassidy on his hot lap in the groups stage.
