After pipping Vettel with a lap of one minute 23.599 seconds in the first practice, Hamilton shaved nearly a second off that in FP2, his quickest lap clocked at 1:22.600.
His Mercedes team mate Valtteri Bottas was 0.048 seconds off the time of Hamilton, who had a yawning 0.800 seconds gap to Max Verstappen in third, with Red Bull's other driver, Pierre Gasly, a further 0.042 seconds behind in fourth.
"I really have a positive buzz from driving the auto today".
"The auto feels like it's in a similar place to where it was in Barcelona, which is positive coming to a different track".
"You get to a non-power sensitive track like Mexico a year ago or Monaco and they're right there, locking out the front row".
His new teammate Charles Leclerc also had a big spin late in FP2 and managed only the ninth fastest time in an underwhelming debut for the Scuderia.
Ferrari hope to work out the problems and get their bolted to the ground version of the SF-90 that we saw in the winter testing, setting their eyes on Qualifying on Saturday. Although, Vettel did not seem to be anxious at all saying there was plenty of lap time still to be found in the auto.
"It was a tricky day for us".
"With Red Bull at the end of the day, no risk no fun", he said. I think for us we are not where we would like to be, not in terms of lap time but in terms of vehicle feel and handling.
"If we can get that confidence and that groove back, there is a lot of lap time in that around here", he added.
"By the time you finish the testing, the cars are ready to be shipped directly to Melbourne, so I think it's really by here that we start understanding who is the fastest".
Alfa Romeo's Kimi Raikkonen was fifth quickest - just 0.099secs behind his former Ferrari team-mate Vettel.
It looked like being a tight midfield battle, however, with both Renaults nipping at Raikkonen's heels.
The Renaults of Nico Hulkenberg and Daniel Ricciardo were sixth and seventh respectively.
British-born Thai debutant Alexander Albon had a tough day, crashing his Toro Rosso to lose his front wing and cause a brief halt in the first session.
There's no shortage of talent behind the wheel of the two cars, with debutant George Russell winning the GP3 title in 2017 and the Formula 2 championship in 2018, while Robert Kubica is a former grand prix victor, returning to the sport eight years after his near-fatal rally accident.