"We have been right on the edge with engine temperature, not quite always there with pace, so the races you aren't completely sure about are the ones that feel the best (to win)," team boss Ross Brawn told the BBC.
Shanghai winner Vettel now trails Button for the title by 13 points, while a further 3.5 points adrift is Jarno Trulli, who after scoring pole position in the Sakhir desert finished 2 seconds adrift of Vettel to complete the podium.
In the presence of big cheese Luca di Montezemolo, Ferrari at least opened its points account, even though Kimi Raikkonen 3 points in Bahrain leaves the famous Italian team just ninth in the constructors' standings. Felipe Massa was just 14th and lapped, apparently with KERS problems and after having to pit for front end damage.
Both BMWs also displayed battle-damage at the end of 56 laps, and only beat Williams' retired Kazuka Nakajima to the chequered flag.
Last year’s world champion Lewis Hamilton finished in fourth, one spot ahead of Button’s teammate Rubens Barrichello.