Verstappen had set the pace in the opening session when he lapped Zandvoort's seaside circuit, the grandstands packed with his orange-clad fans, with a best time of one minute 11.852 seconds.
Norris was fastest overall, however, with a lap of 1:11.330 in the late afternoon, 0.023 quicker than the double Formula One world champion.
While the Briton went top, McLaren teammate Oscar Piastri was involved in a double Australian crash with AlphaTauri's Daniel Ricciardo.
Piastri hit the tyre wall early on at the banked turn three and Ricciardo, with nowhere else to go, followed him into the barriers and red flags were waved.
Ricciardo looked to be in some pain as he struggled to get out of the car and was taken to hospital for checks on his wrist.
Verstappen is chasing a ninth win in a row on Sunday to equal now-retired Sebastian Vettel's decade-old record.
He leads Mexican teammate Sergio Perez by 125 points after 12 of 22
Aston Martin's Fernando Alonso was second quickest in session one, 0.278 slower than Verstappen, with Mercedes seven times world champion Lewis Hamilton third.
Perez was fourth on those timesheets, 0.471 slower than his teammate, with Williams' Alex Albon fifth and Norris sixth.
Albon was third in session two with Hamilton fourth and AlphaTauri's Yuki Tsunoda fifth with Alpine's Pierre Gasly sixth and Perez seventh.
Dominant Red Bull have won every race this season, and the last 13 in total, while Verstappen is chasing his third successive Dutch Grand Prix win.
Haas's Nico Hulkenberg spun off into the gravel, nudging the tyre wall with his front wing, and brought out red flags in the first session.
"The only problem is this was the new front wing and we don't have a lot of them," team boss Guenther Steiner told Sky Sports television.
Aston Martin's Lance Stroll, who skipped media duties on Thursday due to an infection, failed to set a lap time in the first session after reporting a 'funny noise'.
The team investigated a suspected power unit issue and Stroll returned to set the eighth-best time in session two.
Israeli Robert Shwartzman replaced Spaniard Carlos Sainz at Ferrari for the opening session, in line with regulations requiring teams to run young drivers during the season, and was 19th and 2.951 off the pace on medium tyres.
Sainz was only 16th in session two with teammate Charles Leclerc 11th.
