Vettel inexplicably sustained a puncture just two corners into the 55-lap Abu Dhabi Grand Prix, leading to a premature end for the 24-year-old for the first time in 20 races.
Vettel had won the only two previous races at the Yas Marina track, but his shock incident freed Hamilton to take the chequered flag and end a wretched run of form since his last win in Germany.
To say Vettel's exit came out of the blue would be an understatement, notably as he made the perfect getaway from his record-equalling 14th pole this year in his all-conquering Red Bull.
But as he cornered into the slight kink that is turn two, the right rear tyre bizarrely punctured, sending him into a spin off the track and onto the grass.
McLaren star Hamilton must have thought Christmas had come early as he led the remainder of the field past Vettel's stricken car.
Vettel managed to limp back to the pits, but the damage sustained to the floor, exhaust and wishbone was too severe for the German to continue, leaving him thumping his steering wheel in frustration.
Red Bull have since confirmed there was nothing on the telemetry on the formation lap that suggested any kind of issue, and it will now be down to tyre supplier Pirelli to assess what went wrong.
After that, Hamilton drove one of those faultless races we all know he is capable of, but so rarely he has displayed this year.
Alonso, who made a lap one move on Button to move up to second, at times threatened, but instead Hamilton was controlled and composed as he made it 17 wins in his F1 career.
There was perhaps a slight moment of consternation when he pitted first onto the harder, slightly slower medium compound tyre with 15 laps to go, whilst Alonso stayed out on the faster soft rubber.
But in the end it mattered little as the Spaniard in his Ferrari emerged behind Hamilton, and from then on it was a stroll to the line, the 26-year-old dedicating the win to mum Carmen who has been here this weekend to celebrate her birthday, which was on Friday.
It was Button who ended up having the toughest time, primarily as he lost his KERS power-boost system for around 25 laps which meant he fell behind the leading duo.
In the end it was the fact Red Bull opted for a three-stop strategy for Mark Webber that propelled him onto the podium.
On his final set of soft tyres, Webber did all he could to open up a gap over Button, but it was never going to be enough.
The Australian pitted at the end of the penultimate lap, but he emerged around nine seconds behind Button, the 31-year-old in the top three for the seventh time in the last eight races.
It also means Button has won the battle of Britain within McLaren, with Hamilton unable to now close the gap on his compatriot, so losing to a team-mate for the first time since he entered single-seater racing in 2001.
Behind the leading quartet, Ferrari's Felipe Massa was fifth, followed by Mercedes duo Nico Rosberg and Michael Schumacher.
Force India pairing Adrian Sutil and Paul di Resta were eighth and ninth, with Sauber's Kamui Kobayashi claiming 10th.
Hamilton described himself as "ecstatic" and "fantastic", adding: "That was one of my best drives of my career.
"I looked after my tyres, I managed the gap, and the team did a great job, so I'm happy to be back up here. I can now get on my flight tonight and smile."
Asked if he was back on track after all his troubles, he said: "I don't know. It's early days.
"We've a great race in Brazil coming up, so I just need to try and keep the momentum."
Alonso also felt he enjoyed "a fantastic race", adding: "I had a very good start, a good first lap and the fight with Jenson.
"Then after the problem with Sebastian, I fought with Lewis, and at the last stop we stayed out two laps longer than Lewis.
"But in the last stint he had a bit more pace, so even if I had got ahead in the second stop, we probably wouldn't have won, but it has been a good weekend."
As for Button, his KERS issues proved a hindrance as he said: "On about lap 13 or 14 it went.
"I had to fend off Webber and Massa, which was interesting, and then I eventually got it back.
"But then it went again and I had to keep resetting it, which means it was very tricky, so coming home third I'm pretty happy."