The only driver still to score a point after 12 races this season, Latifi topped the timesheets for the first time in his career with a lap of one minute 41.480 seconds as the chequered flag fell.
His lap was 0.661 seconds quicker than Ferrari's Charles Leclerc (24), who had been top until that point and set to complete a practice sweep for the Italian team, even if the time was meaningless.
The team's reaction on Twitter said it all: "WHATTTTTTTTTTTTTTTTTTTTT".
Williams team mate Alexander Albon (26) was third fastest, again thanks to the improving track conditions after heavy rain early in the session, with Red Bull's championship leader Max Verstappen (24) fourth.
Leclerc and Verstappen set their times before the Williams drivers.
Red flags came out with nine minutes to go after Aston Martin's four-times world champion Sebastian Vettel (35), who on Thursday announced his retirement at the end of the season, spun off backwards into the tyre wall at turn 10.
The German screamed in anger and frustration and apologised to his team.
The session at the Hungaroring then resumed with four minutes left on the clock and the sun shining.
Leclerc had also spun earlier, with drivers struggling for grip in the conditions.
"These tyres are just not working at all, they're so cold," complained Mercedes George Russell.
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