Lewis Hamilton completed the podium at the Barcelona-Catalunya circuit for the Mercedes seven-time former champion's first podium of the season.
The racing may be closer than the past two seasons but Verstappen always seems to pull it out of the bag when it matters most.
This was his 61st career win, seventh of the season, and fourth at the track where he first shot onto the F1 scene as a teenager in 2016.
And it pushed him another step further to a fourth straight title with Austria and Silverstone coming up over the next two weekends.
Fourth-placed George Russell in the other Mercedes enjoyed a stunning start.
With Verstappen to the left of Norris, and Russell to the right of him in the charge into the first turn at the end of the long straight, the pole-sitter came out the loser.
As Norris grappled with Verstappen, Russell, unsighted, pulled out from fourth on the grid to take command.
Verstappen raced in second from Norris with Hamilton in fourth.
Two laps later, at the end of the straight, Verstappen made the decisive move of the race.
He was told by his race engineer "Might be our best opportunity Max" and the Dutch ace needed no second invitation, producing a beautiful pass to deprive Russell of the lead, surging over one second clear of the Briton, with Norris less than a second back.
In the first flurry of pit stops after around a quarter of the 66-lap race, Russell had a slow stop, emerging in eighth as Verstappen led by almost five seconds.
Hamilton had a quicker stop than his teammate as Verstappen headed in for a change of tyres, returning to the circuit in fourth behind yet-to-pit Norris.
A feisty Hamilton zipped past home hero Carlos Sainz's Ferrari and up to sixth at turn one, with contact between the pair.
"He touched me, he ran me off," complained Sainz, in what looked like a fair and square racing incident.
Norris and his team were trying a different strategy, staying out longer before a new set of rubber.
He eventually 'boxed' for fresher tyres, to slot back in behind Sainz in sixth.
At halfway it was the familiar presence of Verstappen with a six-second gap from Russell, from Norris, back in third after a straightforward overtake past Hamilton.
'We need to push Max'
A few laps later Norris bested Russell after a bit of nip and tuck between the pair to leave only Verstappen ahead of him, albeit around nine seconds up the road.
Russell promptly pitted as the race entered its business stage, Norris chipping away at Verstappen's lead.
On lap 45 Verstappen came in for a second time, as Norris followed suit, setting up a compelling conclusion in Catalonia.
Norris had over six seconds to make up on his Red Bull rival with 15 laps left as Hamilton moved past his teammate to put himself in the running for his first podium of the season.
"We need to push to the end now Max," Verstappen's engineer urged on the team radio, who took the chequered flag at one of his favourite tracks by a little over two seconds from Norris.
Verstappen heads to Red Bull's home race in Spielberg in a week's time with a 69-point lead over Norris, with Ferrari's Charles Leclerc, fifth on Sunday, third, two points further back.
