The 25-year-old Dutchman led from lights to flag to come home 24 seconds ahead of revitalised seven-time champion Lewis Hamilton and George Russell, in their much-improved Mercedes' cars.
It was Verstappen's third consecutive win, his third in Spain, his fifth in seven races this season and the 40th of his career, achieved despite receiving three official warnings for exceeding track limits.
"It's such a big pleasure to drive a car like this," said Verstappen.
"And it showed again today. We were on different tyre strategies out there today and mostly I was on the right one! And to win here is incredible."
Hamilton's second place provided him with his 11th podium finish in Spain, where he has won six times.
"Oh, man, what an awesome crowd and result," said Hamilton. "And I didn't expect that so hats off to the team and our factory for pushing us so close to the 'Bulls. We are chasing them down -- and George did a great job too today."
Russell said he was surprised to finish third after starting 12th. "Kudos to the team for that," he said. "I had a great car today."
Verstappen's Red Bull team-mate Sergio Perez battled through the field, after starting 11th, to finish fourth ahead of Ferrari's home hero Carlos Sainz, Lance Stroll and his Aston Martin team-mate two-time champion Fernando Alonso, who was unable to extend his streak of podiums on home ground.
The race began in hot conditions with an air temperature of 25 degrees and the track at 42, but gathering clouds threatened. The risk of rain was 40 percent.
Verstappen made a clean start and resisted Sainz into the first corner before, behind him, Hamilton swept round Norris, only for the McLaren to make contract under braking at Turn Two.
Norris's front wing was damaged, requiring a pit-stop, but Hamilton escaped serious damage. The collision gifted Stroll third place, but this was not to be Aston Martin's day.
Russell also left the track on the opening lap, at the first chicane. He was not penalised, despite gaining five places from the start.
Verstappen stamped his authority on proceedings and by lap 11 led Sainz by 5.3 seconds with Hamilton, thanks to a sweeping pass on Stroll on lap eight, in third.
By mid-distance, Verstappen led by 13.7 seconds ahead of Hamilton, who was six clear of Sainz and pulling away. Russell, fourth, passed the Spaniard under braking at Turn One on lap 35, confirming the 'silver arrows' outright speed in the sunshine.
Verstappen, who had complained of sliding on his worn hards, came in for his final stop on lap 53, taking softs to reach the finish. He was more than 16 seconds clear of Hamilton when he re-joined for his cruise to the flag.
With six laps remaining, he was shown a third black-and-white warning flag. "We can't afford anything," his team warned him as he enquired about his fastest lap.
Verstappen responded with a lap in 1:16.330, the fastest. "OK, now can you bring it home within the white lines," came race engineer Gianpiero Lambiase's response.