Verstappen's cruise from pole position, with Perez taking the chequered flag 11.9 seconds behind, was his first win in Bahrain and also the first time the double champion had triumphed in the opening race of a campaign.
"Very lovely that, really good result. We had good race pace," Verstappen told the team on his slowing down lap. "Very happy with that. Thank you guys.
"That's exactly the start to the season we wanted and needed. A perfect one-two".
Ferrari's Charles Leclerc was running in third place when he slowed and pulled over 17 laps from the end, shouting "No, no, no! No power" over the team radio.
Veteran double world champion Fernando Alonso then passed Carlos Sainz's Ferrari with a thrilling wheel-to-wheel move 12 laps from the end to secure the final place on the podium for Aston Martin.
"This is a lovely car to drive," the 41-year-old Spaniard, the oldest driver in the race, told his jubilant team.
"To come here and finish on the podium in the first race of the year, it is amazing what Aston Martin did over the winter to have the second best car on race one. This is just unreal," he told the crowd after the finish.
Seven times world champion Lewis Hamilton was fifth for Mercedes with Canadian Lance Stroll giving Aston Martin a bumper points haul with sixth.
It was a remarkable drive from the young Canadian, who broke both his wrists and big toe in a cycling accident in Spain two weeks ago.
George Russell was seventh for Mercedes with Valtteri Bottas eighth for Alfa Romeo and Pierre Gasly ninth on his Alpine debut after joining from AlphaTauri and starting the race in last position.
Alex Albon took the final point for a markedly more competitive-looking Williams.
Australian Oscar Piastri meanwhile retired 14 laps into his debut with his stricken McLaren wheeled into the team garage after suffering an apparent electronics issue.
The 21-year-old had complained of gearbox problems and mechanics swapped the steering wheel when he pitted but he could not restart.
