The Australian rookie set a 1m28.612s with five minutes left in the session to top the timesheet, having also taken pole for Virtuosi Racing at the season opener in Bahrain.
Vips, who took part in his first Formula 1 practice session for Red Bull earlier on Friday, had been running in 21st until a last-minute flying lap put him up to second by just 0.02s.
Frederik Vesti will line up third for ART Grand Prix, with the Mercedes junior having also waited until the last few minutes of the session to put in his quickest lap, a 1m28.852s.
Prema Racing’s Jehan Daruvala was first to lead the Friday evening session, setting a 1m29.572s, with Clement Novalak and Jake Hughes in second and third.
While much of the field pitted after the first 10 minutes, several drivers – Felipe Drugovich, Doohan, Marcus Armstrong and Richard Verschoor – ran on an alternate strategy and ran in the gap.
Drugovich took provisional pole on his first attempt with a 1m29.190s before Doohan bettered his time by just 0.05s.
But his first reign at the top of the times was ended by Daruvala, who was first to break the 1m28s barrier with a 1m28.884s.
His teammate and reigning FIA Formula 3 champion Dennis Hauger improved from eighth to fourth with his second run, setting a 1m29.381s.
The pair both exited their cars with 10 minutes remaining, leaving the likes of Doohan and Vesti to push them down the order. Daruvala finished the session fourth, with Hauger in 14th.
While the Prema pair watched on, Doohan set his pole time, beating Daruvala by 0.2s, before Vesti and Vips joined him in the top three.
Drugovich and Pourchaire are under investigation for impeding after the Frenchman claimed the Brazilian got in his way at Turn 1, while several other drivers were noted as a traffic melee similar to that seen earlier in F3 qualifying ensued.
Campos Racing’s Ralph Boschung was forced to withdraw from the weekend after suffering from “significant neck pain” which started at Imola.
The team said Boschung was “confident” he would be able to race this weekend, but he realised during free practice he “could not drive at the best of his abilities” and withdrew in a bid to fully recover by next weekend’s round in Monaco.
Drugovich will start on pole for Saturday's reverse-grid sprint race, with Calan Williams in second and Hughes in third.
