Red Bull decided to suffer the punishment for taking on a fifth engine at Spa where overtaking is easier than other circuits, and where the three-time champion won from 14th on the grid two years ago.
Verstappen, without a win in three races, will have his work cut out this time however, with McLaren bringing their Hungarian form to Belgium after Piastri won his first F1 GP last weekend, ahead of Norris.
That win may have been overshadowed slightly by Norris' delay in accepting team orders to allow Piastri to retake the lead, but the pair have clearly put that behind them, and Norris posted the fastest time of one minute and 42.260 seconds.
Norris, second in the drivers' championship, was eighth fastest in the first practice session but overtook his teammate's impressive time in the second session to finish 0.215 seconds ahead of Piastri.
Despite leading the way, Norris is still not completely at ease with his McLaren.
"I have not felt comfortable today with the car. Hopefully, I wake up tomorrow and feel more comfortable. We'll try to improve a few things," Norris said.
"I know it looks good on the timesheets but I didn't feel super-comfortable going out and doing it. Hopefully, I get in more of a rhythm out there.
"We prepared well. We have a good set-up. It's working. Just from my side, feeling like I can go out and nail it? I'm not quite there yet."
Verstappen posted the fastest time, one minute and 43.372 seconds, in the earlier session, but ended the day just behind Piastri and 0.217 seconds adrift of Norris.
Ferrari improved their standings in the second practice, with Charles Leclerc moving from sixth to fourth and Carlos Sainz up from ninth to fifth, which came at the expense of Mercedes pairing George Russell and Lewis Hamilton.
Russell dropped from fourth to sixth with Hamilton, who has won the Belgian GP four times, falling to 10th from fifth in the first session, 1.259 seconds behind Norris.
Esteban Ocon, who will drive for Haas next season, had significant issues with his Alpine car, where a suspected water leak saw him complete just one lap before abandoning the first practice, but he finished the day with the seventh fastest time.
Kevin Magnussen of Haas, still without a drive for next year, posted the eighth fastest time while Sergio Perez continues to struggle for Red Bull, and ended the day in ninth, over one second slower than Verstappen and 1.244 off Norris.
The rain stayed away on Friday but is expected to fall on Saturday at Spa for the final practice session and qualification. RB's Yuki Tsunoda will start at the back of the grid on Sunday after his engine penalty.