The pair rose to the top midway through the session courtesy of their single-lap pace, heading a surprise performance by Nico Hulkenberg.
Carlos Sainz was fourth, just under six-tenths slower than Norris, with Lewis Hamilton all but equalling the Ferrari driver to sit fifth.
The second hour of running welcomed back the usual contenders, with the six rookie interlopers from the opening session having handed back their cars.
That saw Max Verstappen for Red Bull Racing and Carlos Sainz at Ferrari out on track early as they looked to make up for lost time.
Sainz promptly shot to the top of the timesheets inside the opening 10 minutes to underscore the potential the Scuderia demonstrated in Free Practice 1.
McLaren was also quick once more, Norris inching ahead courtesy of a 1:24.332s to sit two-tenths clear after 20 minutes.
Verstappen’s early pace was encouraging, though he was far from happy with the car.
His major complaint was the front axle, though also that he had no power at low revs from his Honda power unit.
Mercedes was initially less present at the top of the timesheets, with Russell just under a second off the pace before the single-lap runs began.
At the other end of the timesheets was Jack Doohan, who continued to work through his program, logging nine laps in the opening half hour to sit 2.1s off the outright pace.
He was also a second away from his Alpine team-mate Pierre Gasly, though that meant little as far more important than lap times was time on track.
As has become the norm in Free Practice 2, qualifying simulations began at the halfway point.
That process saw Red Bull Racing exposed, Perez 1.038s off the pace while Verstappen slipped to 17th at the chequered flag, 1.081s adrift.
However, there is more pace than that in the Red Bull Racing and better things are expected of them come final practice, let alone qualifying.
McLaren sat proudly atop the standings after the qualifying simulations, Norris fastest from Piastri with Sainz third.
Encouragingly, Hamilton sat fourth, scarcely a tenth away from the third-placed Ferrari.
Charles Leclerc did not feature towards the top of the timesheets.
With a 10-place penalty looming over him, the best he can hope for is to start 11th.
The focus for him was therefore setting up a car that will work in traffic and allow him to pass come Sunday’s race.
Of course, there was still a need for single lap pace, as Ferrari wants Leclerc as close to the front as possible even once the penalty is applied.
Away from the top four teams, Haas showed promising pace with Hulkenberg improving with a comparative late qualifying simulation to steal the third fastest time, between Piastri and Sainz, with Kevin Magnussen eighth.
Liam Lawson was just outside the top 10, just 0.006s away from Yuki Tsunoda in 11th place in an encouraging display off the back of a dismal weekend for the squad in Qatar.
Doohan ended the session 19th, though more importantly only four-tenths shy of the in-form Pierre Gasly in the other car.
It can therefore be regarded as a promising performance from the Australian debutant who banked laps and didn’t put a foot wrong – a pinched brake or two excused.
McLaren however ends Friday with the upperhand, though Ferrari and Mercedes are within touching distance.
Red Bull Racing remains something of an enigma though nothing it displayed during the day’s two hours suggested they’re a match for the top three teams.
An hour of practice remains, starting at 14:30 local time on Saturday (20:30 AEDT).
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