Defending champion Hamilton seemed on course to cruise to the chequered flag at Melbourne’s Albert Park after winning the dash to the opening bend and building up a comfortable lead over the pack.
But the curtain raiser turned on its head in the space of a frenetic few laps when Vettel leapfrogged Hamilton following the deployment of a virtual safety car after Romain Grosjean stopped on track.
Hamilton had already made his one stop for tyres, but Vettel took advantage of the VSC - in which the drivers have to run at restricted speed - to pull into the pits and emerge ahead of the Englishman.
Hamilton led the inquest over the team radio, in which Mercedes replied: “We thought we were safe, but there was obviously something wrong.”
The suspicion here was that Mercedes should have instructed Hamilton to ensure he was closer to Vettel to cover off the possibility of a virtual safety car period.
Hamilton attempted to make his move on the Ferrari in the closing stages, but after vowing to “go for it”, he locked up his tyres, ran over the grass, and lost further time from which he would not recover.
Kimi Raikkonen held off the challenge from home favourite Daniel Ricciardo to complete the podium places, while McLaren’s Fernando Alonso finished fifth for McLaren. Max Verstappen was sixth for Red Bull.
On a bleak day for Mercedes, Hamilton’s team-mate Valtteri Bottas finished only eighth after starting 15th following his qualifying crash.
The narrow confines of the temporary Albert Park circuit makes overtaking nigh on impossible and, after Hamilton roared off the start line, the 33-year-old Briton appeared certain to open the defence of his championship with a victory.
Indeed the race was passing by with relatively little incident, but a double retirement by both Haas cars changed the course of proceedings.
On lap 23, Kevin Magnussen, running in fourth, was the first to fall after the American team failed to properly fit his rear-left tyre.
Then, inexplicably, the Haas pit crew made another error only two laps later, after an identical mistake on Grosjean’s car. This time it was the front-left tyre which was not on securely, and the Frenchman had to pull over on track.
His stoppage led to the deployment of the VSC, and Vettel, 11 seconds clear of Hamilton - with the Briton already having stopped - dived into the pits to take on fresh set of tyres. He exited in the lead and half-a-second clear of Hamilton.
“What just happened, guys?,” a perplexed Hamilton quizzed over the radio. “Why did you not tell me Vettel was in the pits? Was that my mistake? Was I supposed to go quicker through the safety car?”
The reply from the Mercedes pit wall suggested Hamilton was not at fault.
With the inquiry still taking place, the VSC was replaced by the safety car proper as the marshals removed Grosjean’s stricken car.
The safety car came in a matter of laps later, but Hamilton never troubled Vettel as the German took the opening spoils of the new campaign.
“A big congratulations to Sebastian and Ferrari,” Hamilton said. “They did a better job. We will go back to the drawing board and work on it, but we have great pace.
“This is one awesome circuit but it is so hard to overtake. At the end we decided to fight another day, save the engine, and try to get the points elsewhere.”
Vettel, who secured his 48th career victory, added: “We are a little bit lucky today. Lewis did a great lap and deserved pole yesterday. We got lucky today, but we will take it.
“We are not where we want to be with the car. It gives us a good start, a good win, and fresh motivation for the coming weeks.”