Mexican Sergio Perez was runner-up under the Jeddah floodlights, last year's winner taking the chequered flag 13.643 seconds behind his triple world champion teammate.
It was the first time Verstappen, winner of a record 19 of 22 races last year, has won the first two races of a season.
Charles Leclerc finished third for Ferrari, taking a bonus point for the fastest lap and earning his first podium of the season.
The victory was a ninth in a row for Verstappen, dating back to Japan last September, and 56th of the Dutch driver's career.
It was also his 100th career podium while Red Bull's 115th win lifted them ahead of Williams in fourth place on the all-time lists.
"Overall, a fantastic weekend for the whole team and myself. I felt really good with the car and it was the same in the race," Verstappen said.
Britain's Oliver Bearman, making his F1 race debut as Ferrari's youngest-ever rookie at 18 years and 305 days old after Spaniard Carlos Sainz was sidelined by appendicitis, finished seventh and was voted Driver of the Day.
"Today he's been incredible," said Leclerc of his temporary teammate. "It's hugely impressive and I'm sure he's extremely proud. Everybody has noticed how talented he is and I'm sure it's just a matter of time before he's in F1."
BRITISH DRIVERS
Oscar Piastri was fourth for McLaren, with Fernando Alonso fifth for Aston Martin and George Russell sixth for Mercedes and the first of four British drivers following each other across the line.
McLaren's Lando Norris was eighth and seven-time world champion Lewis Hamilton ninth for Mercedes with Nico Hulkenberg taking the final point for Haas.
The safety car was deployed on lap seven after Aston Martin's Lance Stroll hit the wall and then crashed into the barriers at turn 22.
The Canadian walked away unhurt as all but four drivers, including Norris and Hamilton, dived into the pits.
Norris, who was later cleared of a suspected jumped start off the grid, led when the new Aston Martin Vantage safety car returned to the pits on lap 9 but Verstappen was back in front by lap 13 and pulling away.
Perez was handed a five-second penalty for an unsafe release from his first pitstop and Haas's Kevin Magnussen collected a 10-second penalty for causing a collision with Williams' Alex Albon.
The Dane was later handed another 10-second penalty for leaving the track and gaining an advantage but his main role was to create a sufficient gap behind Hulkenberg for the German to be able to pit and still finish with a precious point.
Alpine's Pierre Gasly was told to pit and park on the opening lap due to a suspected gearbox issue, becoming the first retirement of the season after all 20 cars finished the opener in Bahrain a week earlier.
