Alonso's pit stop on the 24th lap then proved disastrous as pit crew struggled to change the left front tyre which had previously been damaged in a slight collision.
The Spaniard rejoined the race in 14th place - far off the pace, but had to give up shortly afterwards with a wheel problem.
Fisichella and Raikkonen both pitted for the last time in the 30th lap with the Ferrari again managing to come out fractionally first, but then failing to open up any real gap.
Vettel took over the lead when the two leading cars went into the pits and the young German tried to use the open lane to his advantage to gain some ground on the leading cars.
He managed to come out ahead of BMW Robert Kubica in third after his final pit stop and then clawed his way closer to the two leading cars, but in the end simply ran out of time to overtake Fisichella or Raikkonen.
Kubica finished fourth ahead of his team-mate Heidfeld, while Heikki Kovalainen in a McLaren took sixth place from Brawn GP's Rubens Barrichello who managed to cross the finishing line even though his car was leaking oil for the final laps.
The final championship point went to German Nico Rosberg in a Williams.
Button maintains his lead with 72 points from team-mate Rubens Barrichello, who has 56 points. Vettel is third with 54 points.
The next race is the Italian Grand Prix in Monza September 13.