"We've had a great three years here. Mark drove flawlessly. The weather was a real concern, but he did a great job to do what he needed to do," said Newey, whose team are the first to win two races this year.
Vettel, last year's winner, had moved up from ninth place at the start by completing 46 laps on his first set of tyres.
Hamilton dropped from third on the grid to finish fifth, losing his two places in the pits thanks to a stop that was six tenths of a second slower than those of Vettel and Alonso.
"The target was to try to finish in front of Sebastian and Lewis as they are with us in the championship," said Alonso. "We took Hamilton at the stop with a perfect time and a perfect stop again, so well done to the team."
In Image: Red Bull driver Mark Webber of Australia celebrates with champagne after winning the Formula One Grand Prix