But Charles Leclerc and Ferrari endured more reliability pain with an engine issue prompting last year's championship runner-up to stop on the side of the track.
Verstappen made the perfect start to defend his lead into the first corner but behind, a sluggish start for team-mate Perez allowed Leclerc and Sainz to pounce.
One Ferrari went through but the Spaniard was muscled out to the inside as Leclerc and Perez juked for position.
Alonso was hit by team-mate Lance Stroll at turn four but somehow both Aston Martin's escaped damage.
Verstappen soon sauntered into a commanding position, with a 10-second lead over Leclerc by the end of the first pit stop window on lap 18.
An alternate strategy from Red Bull to use a second set of soft tyres during the second stint saw Perez close up to the back of Leclerc, passing the Monégasque with ease into the braking zone at turn one on lap 26.
Leclerc had settled for third with a conservative strategy for the final stint of the race and when 12 seconds down on Perez, the SF-23 pulled to the side of the road at the exit of turn 13, triggering the virtual safety car on lap 41.
A suspected engine issue was the last thing Ferrari needed after reliability issues hampered its charge last year, with Leclerc's energy store being swapped to its second and final free component ahead of the race.
Sainz was 27 seconds down on Perez with Alonso swarming his rear wing, leaving Red Bull in a comfortable position, Verstappen picking up where he left off last year.
Alonso was the story of testing and the first two days of running with the Aston Martin debutant qualifying fifth at the tender age of 41.
His contact with Stroll at the start of the race left him behind both Mercedes drivers but after jumping George Russell at the first round of stops, Alonso set after old nemesis Hamilton.
After failing with his first attempt on the W14 at turn four on lap 37, the two-time champion entered for move of the season with a daring switchback from outside to in at the double-apex turns nine and ten, leaving Hamilton powerless to defend.
Sainz was able to hold off Hamilton to finish fourth and at least retain third-best on the road.
Stroll was comfortable ahead of Russell to take sixth - a heroic effort after recovering from two broken wrists and a broken toe sustained just two weeks ago.
Valtteri Bottas guided his Alfa Romeo to eighth ahead of Pierre Gasly, who rescued his weekend and some dignity for Alpine given the French manufacturer's difficult start to the season.
Alex Albon held on to secure a point for Williams despite late pressure from AlphaTauri's Yuki Tsunoda, while Logan Sargeant impressed on debut to finish 12th.
Kevin Magnussen secured 13th for Haas ahead of Nyck de Vries and Nico Hulkenberg, who picked up a five-second penalty for abusing track limits.
Zhou Guanyu pitted late on to drop to 16th, but set the fastest lap with his final effort on fresh tyres.
McLaren endured a horrific first race of the season as Oscar Piastri and Lando Norris were both hit with reliability issues.
Debutant Piastri saw his race end prematurely with an electrical issue on lap 13, returning to the pits and failing to arrest the issue with a steering wheel change.
Norris, meanwhile, six-stopped with McLaren required to top up his MCL60 with pneumatic pressure.
Esteban Ocon picked up a plethora of penalties before his retirement, having been out of place on the grid, then failing to correctly serve the five-second penalty to add another 10 seconds, and a final five seconds added for speeding in the pits.
The Frenchman joined Leclerc and Piastri in failing to finish.
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