It was a hat-trick of titles for the 25-year-old German, who had come into the last race of the season with a 13-point over Ferrari's Fernando Alonso and pipped his closest rival by just three points.
Red Bull's Vettel had 281 points after the 20th and final round while Alonso, who drove splendidly to finish second at the race had 278.
Vettel overcame a horrendous start, where he endured a lap 1 accident which pushed him to back of the grid, to finish a superb sixth and become only third driver in F1 history to won three consecutive drivers title.
Vettel erased record of legendary Brazilian driver Ayrton Senna, who had become the youngest triple champion at the age of 31 years and 227 days. Senna, who died in an accident during the San Marino Grand Prix in 1994.
Senna won the drivers' championship in 1988, 1990, 1991.
Vettel, who had a very strong second half with four straight wins -- Singapore, Japan, Korea and India.
Alonso needed a miracle of sorts to pip Vettel to the title and it almost happened but for a great drive by Vettel he had to content with runners-up finish.
Ferrari had a fantastic season-end with both the drivers on the podium as Felipe Massa was third, followed by Mark Webber ahead of Sahara Force India's Nico Hulkenberg.
It was a an unfortunate last race for Hamilton with McLaren as he crashed out after leading the race, following a contact with Nico Hulkenberg in lap 49.
The race also marked the second retirement for seven-time world champion Michael Schumacher, who finished seventh after qualifying in 14th place.
The 43-year-old German had joined Mercedes in 2010, having first retired in 2006 with Ferrari.
His second stint has not been quite successful as he failed to win a single race in three seasons in deep contrast to his record 91-race victories in first stint, which began in 1991.
Behind Schumacher was Jean-Eric Vergne, Kamui Kobayashi and Kimi Raikkonen, who finished third in drivers standing with 207 points.
It was great a chance for Hulkenberg to end his association with Sahara Force India with a podium finish but his over ambitious overtaking move in lap 49 not only ended Hamilton's race but also got him a drive-through penalty, which cost him four places.
The young German had snatched lead from Hamilton in as early as lap 19 in the 71-lap race.
Vettel could not have more disastrous start as he was hit from back by Bruno Senna which damaged his car and left him at the back of the pack.
Pole sitter Hamilton held his position from McLaren teammate Button, who was locked in a good battle with Massa.
Alonso made his way up to third as the Spaniard made a move on Mark Webber in the second Red Bull and his own teammate Felipe Massa on turn one.
However, the slippery conditions were tough to negotiate and Alonso was soon off the track, to fall back to seventh. Hulkenberg took advantage and past Alonso and Webber to go up to third place.
Fortunately for Vettel his car was not damaged to the extent which could end his race and he made an astonishing fightback to zoom up to sixth position.
Both Vettel and Alonso shifted to intermediate tyres via first pit stop, considering the wet conditions.
Hulkenberg meanwhile moved to second between race leader Hamilton and Button and in lap 19 the German used his KERS to snatch the race lead.
Vettel and Alonso were locked in a tense title battle with the German in fifth position right at the back of the Spaniard.
Some debris on the track resulted Nico Rosberg suffering a puncture and it brought Safety Car into the race. Hulkenberg straight away went to the pit lane and held his lead from Button, who too went to pits at the same time.
However, it erased Hulkenberg and Button's huge 47-second lead from the rest of the field.
The Force India driver started to struggle with his tyres and his gap with Hamilton began to reduce. In lap 49, at turn six, the German slipped a bit and it was enough for Hamilton to snatch back the race lead.
However, disaster was waiting for Hamilton as Hulkenberg tried to pass him at turn one in lap 54 but lost control, slid, hit him and broke Hamilton's front suspension, ending the Briton's race.
It pushed Alonso to third with Vettel at seventh at time and Button was leading the race. The rain started to lash the circuit and it became quite a challenge to drive under wet conditions.
Hulkenberg was handed a drive through penalty for colliding Hamilton's McLaren and with that he dropped to fifth.
Alonso moved to second and maintained that position as Paul di Resta's accident in lap 70 brought Safety Car for the second time in the race and the cars finished in the same position.