The Dutchman clocked a one-minute, 43.922 second lap in the closing minutes of the hour-long session to pip Russell by 0.099 seconds.
Lewis Hamilton also pulled out a late flier to go third for Ferrari 0.111 seconds off Verstappen’s pace.
Runaway championship leader Kimi Antonelli, who lost valuable track time to a hydraulics issue on Thursday, was fourth.
Russell, who trails his 20-year-old Italian teammate by 81 points after 14 rounds, has looked dialled in all weekend.
The 28-year-old was fastest in both sessions of running on Thursday and, until Verstappen’s late effort, had looked set to close out his domination of practice with another fastest effort.
Charles Leclerc, who has started the Baku race from pole four times but is yet to win, was fifth for Ferrari ahead of Alpine’s Pierre Gasly in sixth.
McLaren pair Oscar Piastri and Lando Norris were seventh and eighth ahead of Isack Hadjar, making his Red Bull return after missing three races with a wrist injury.
Argentine Franco Colapinto rounded out the top-10 for Alpine.
The session ran without interruptions, but gusty conditions sent several drivers, including Verstappen and Hamilton, skittering across the run-off areas.
Russell very nearly ploughed into the barriers during one such instance but managed to get his Mercedes stopped just in time.
Lance Stroll clouted a barrier and picked up a puncture, continuing a nightmare weekend for Aston Martin.
Both the Canadian and double world champion teammate Fernando Alonso are set to start from the back of the grid thanks to hefty power-unit-related penalties.
The Azerbaijan Grand Prix, the first of a "triple header" of races on consecutive weekends, is being run on Saturday this year with the country marking its Remembrance Day on Sunday.