Racing in Japan for the first time since 2019, the hour-long session saw rain fall throughout - Alonso timing his run perfectly to put his Alpine top of the timing sheet with a lap of one minute 42.248 seconds.
With teams taking their time to head out on track, Nicolas Latifi ran wide as the speeds picked up on a drying track just as Verstappen left the pits for the first time.
He smashed the fastest time by over three and a half seconds as a potential title-winning weekend began in style.
That proved to be his only run of a session which was gradually picking up pace, Alonso eventually setting the pace ahead of the Ferrari pair of Carlos Sainz and Charles Leclerc.
Esteban Ocon was fourth in the sister Alpine while the Haas pair of Kevin Magnussen and Mick Schumacher sandwiched Verstappen - who finished sixth-fastest.
Lando Norris was eighth for McLaren as the Alfa Romeo of Valtteri Bottas - who won here for Mercedes last time out in 2019 - and Verstappen's team-mate Sergio Perez rounded out the top 10.
Times soon began climbing as the rain, which had been lashing Suzuka since early morning, fell heavier.
The Mercedes pair of Russell and Hamilton left it late to head out on track and were caught in the downpour in the latter stages of a session which ended with Schumacher crashing out after the chequered flag had dropped.