Verstappen was comfortably quickest in the opening hour at Albert Park by nearly half a second before Alonso clocked the fastest lap in a rain-affected second.
Aston Martin have been the biggest threat to Red Bull in the opening two races of the season with Alonso taking a podium behind a Red Bull one-two in Bahrain and Saudi Arabia. But the nature of the circuit in Melbourne ought to be the most suited to the Aston to date.
Verstappen had arrived in Australia still complaining of breathing difficulties from a recent illness, and struggled with the handling of the RB19 and slow gear shifts in the opening practice.
Despite that and a late spin at turn four, his time of 1:18.790 comfortably eclipsed the rest of the field with Lewis Hamilton a surprise second initially before tumbling down to 13th fastest during his second 60 minutes on track.
Following the day’s sessions, Hamilton said: “This morning was good, this afternoon not so good. I made some changes that didn’t work. We won’t be competing against the Red Bulls, we’ve the pace to be about fifth.”
In contrast, team-mate George Russell, who has outdriven Hamilton so far this season, struggled in FP1 but had a far better balance with the car in FP2.
But Mercedes said hopes of a leap forward on the grid would not come until Imola towards the end of May at the earliest when they will unveil their first upgrades to the W14.
Team principal Toto Wolff said: “The next three races we won’t be adding any performance. It’s finding the best set-up. We’re not looking for upgrades before Imola and we shouldn’t expect miracles like we’re suddenly more than half a second quicker.”
Alonso again looked very comfortable at the controls of the Aston Martin as he clocked a best lap of FP2, just a tenth of a second slower than Verstappen’s morning time before the rain came down.
The Spaniard and team-mate Lance Stroll were among those to come close to spinning on the intermediate tyres along with the Mercedes duo. Meanwhile, in FP1, Logan Sargeant came to a halt in his Williams while the session was red-flagged following a failure of Formula One’s GPS system.