Alonso's teammate Giancarlo Fisichella moved around constantly in the field, but managed to end up in fifth from sixth on the grid.
Jarno Trulli had a good race, ending up on the podium in third ahead of his teammate Ralf Schumacher, who fell behind after the first round of pitstops.
Meanwhile, Räikkönen's teammate Juan Pablo Montoya had an average race, moving around in the field but still only managing a seventh place.
David Coulthard claimed the final points-paying position in eighth after starting from ninth.
The bottom 6 teams in the 2004 Constructors' Championship were entitled to run a third car in free practice on Friday.