The Briton was eight-tenths clear of Red Bull's Max Verstappen in third, while Ferrari's Sebastian Vettel was only fifth in a low-profile practice for the Scuderia which saw Charles Leclerc more than a second down in ninth.
Mercedes and Haas have an unchanged driver line-up with World Champion Hamilton and teammate Valtteri Bottas aiming high in 2019, and Kevin Magnussen and Romain Grosjean hoping to build on a successful debut season for the Haas F1 team.
Hulkenberg's time signified a much more competitive showing for Renault than in FP1, with Daniel Ricciardo less than 0.1s further back on a 1m23.644s. For me, it's about developing the understanding of the auto and we've made a good start on that today.
He added: "The auto feels like it's in a similar place to where it was in Barcelona, which is positive coming to a different track".
"I think we didn't really get into the groove and into the rhythm and that's quite important around here".
"We didn't have a ideal start for winter testing, so there are a lot of things to be checked".
Don't forget, in recent years Ferrari has made a habit of setting the fastest time in pre-season testing, only for Mercedes drivers to claim the world title.
But four-times champion Vettel painted a gloomier picture, saying his vehicle was not behaving like it had during testing.
"We didn't bring a lot of new parts to the vehicle, but we were able to optimise the package that we have".
"Judging from the performance in Barcelona, it looks like we will have a proper fight on our hands", Mercedes team principal Toto Wolff said to BBC. And with a salary this year mooted at $49 million he's got everything to grin about - Formula One has announced a welcome change to its points scoring system awarding a point to the driver who sets the fastest race lap, something it did in the early years from 1950 to 1959.
Vettel later bolted on softs and put in a lap of 1m23.473s to go fifth fastest, subsequently describing the vehicle as "still a bit wobbly" over the radio.
Alex Albon was 17th, one place behind the second Racing Point of Sergio Perez, and followed up his FP1 crash with a run through the gravel mid-season then a similar spin to Giovinazzi's late on.
"It has been alright".
"It's not doing exactly what I like here and there so that's why I'm lacking confidence".
The other rookie, British-born Thai Alexander Albon, had a hard first day. He slid onto the gravel again in session two and skidded onto the grass.