That mistake allowed Vettel to overtake Button but, somewhat surprisingly, it was Mercedes’ Nico Rosberg who emerged in the race lead after the first round of stops.
It was the start of a period during the race when different tyre strategies evolved and, just like last week in Malaysia, it became difficult to establish just who would emerge in front.
Cars that had just stopped for fresh rubber began moving through the field with ease, then just as fast would suddenly start going backwards as the rubber wore off. It was just a case of waiting for the strategies to play out.
The choice was between a two- or a three- stop and as it turned out, the latter option was preferable. Once all the pit stops were over Vettel was leading from Ferrari’s Felipe Massa, with both men having stopped twice. But Hamilton and Button, on three-stop strategies, were fast closing with fresh rubber.
Hamilton surged past Massa with 11 laps remaining, then picked off Vettel to claim the race lead with a moved which “surprised” the German into the left-hander at Turn Seven. He never looked back.
Button, meanwhile, had made it past Rosberg – who had been told that his fuel levels were critical, although it is unclear how much this affected his pace – and it looked as if he would take the final podium place.
He had not counted on Webber roaring back after a desperately disappointing Saturday in which he qualified 18th on the grid.
The Australian, driving as if his career depended on it – and it does – had stormed through the field on a three-stop strategy, despite having no KERS energy boost device, and with one lap of the race remaining he powered past Button to claim a hugely unlikely podium.
Webber’s finishing time was just seven seconds behind race winner Hamilton. “Maybe the best thing to do is not even take part in qualifying and go from there,” he joked afterwards. “It was a good day for racing and a good day in terms of points for the team."
Vettel admitted his two-stop strategy had been the wrong one but insisted he did not view the day as a disappointment.
"The start was not the best we have had,” he said. “It wasn't a 100 per cent good start so I lost position. We treated the tyres better up to the first pit stop. I came to the box and afterwards came out first. It was a surprise when Jenson went into my garage.
“We came out in the lead and then I think we tried too hard staying on two stops. I saw Lewis coming closer and there was no point defending too hard - he found his way past. We did a couple of mistakes but still finished second so I'm very happy with that.
“We can learn a lot today. I'm the only one with two stops up here so that's something to look into tonight. I was asking questions and not getting any answers, we had a problem with Kers so it wasn't a trouble free race. Once we decided to go two-stop we had to be patient."
The day, though, belonged to Hamilton who, after eight years in China, became the first man to win twice. Bowing to the crowd as he stepped out of the car he flung himself in to the arms of his mechanics in an emotional celebration.
“The strategy definitely paid off for me,” he said. The pit stops were fantastic and the car felt great. I tried to make my tyres last and I tried to push. It is one of the best races I have experienced."
Speaking about the problem he had in the build-up, which had his mechanics sweating as he made it to the grid with just seconds to spare, Hamilton added: "I was a bit worried as the car just wouldn’t start but fortunately everything just came together very quickly. I tried to stay positive.
"There is a long road ahead of us but I’m absolutely over the moon. It feels like a long time since I’ve been sitting here.”
Britain's Paul di Resta said he was content with his weekend in China despite failing to follow up an impressive qualifying display with a points haul.
The Force India rookie has been one of the stars of the early weeks of the season, picking up points at his first two grands prix and lining up eighth in Shanghai - once again getting the better of experienced team-mate Adrian Sutil.
But the race proved a bridge too far for the 25-year-old, who finished in 11th place, just outside the points after a remarkable afternoon which saw position changes and drama throughout the field.
"It was always going to be quite a tough race, starting from where we were," Di Resta said. "We came very close to scoring points, but just missed out at the end when the tyres had gone."
Final positions after 56 Laps: 1 Lewis Hamilton (Gbr) McLaren 1hr 36mins 58.226secs, 2 Sebastian Vettel (Ger) Red Bull 1:37:03.424, 3 Mark Webber (Aus) Red Bull 1:37:05.781, 4 Jenson Button (Gbr) McLaren 1:37:08.226, 5 Nico Rosberg (Ger) Mercedes GP 1:37:11.674, 6 Felipe Massa (Bra) Ferrari 1:37:14.066, 7 Fernando Alonso (Spa) Ferrari 1:37:28.848, 8 Michael Schumacher (Ger) Mercedes GP 1:37:29.252, 9 Vitaly Petrov (Rus) Renault 1:37:55.630, 10 Kamui Kobayashi (Jpn) Sauber-Ferrari 1:38:01.499, 11 Paul di Resta (Gbr) Force India 1:38:06.983, 12 Nick Heidfeld (Ger) Renault 1:38:10.965, 13 Rubens Barrichello (Bra) Williams 1:38:28.415, 14 Sebastien Buemi (Swi) Scuderia Toro Rosso 1:38:28.897, 15 Adrian Sutil (Ger) Force India at 1 lap, 16 Heikki Kovalainen (Fin) Lotus F1 at 1 lap, 17 Sergio Perez Mex Sauber-Ferrari at 1 lap, 18 Pastor Maldonado (Ven) Williams at 1 lap, 19 Jarno Trulli (Ita) Lotus F1 at 1 lap, 20 Jerome d'Ambrosio (Bel) Virgin Racing at 2 laps, 21 Timo Glock (Ger) Virgin Racing at 2 laps, 22 Vitantonio Liuzzi (Ita) HRT-F1 at 2 laps, 23 Narain Karthikeyan (Ind) HRT-F1 at 2 laps
Not Classified: 24 Jaime Alguersuari (Spa) Scuderia Toro Rosso Retired
