Räikkönen climbed through the field to finish fourth, ahead of Jarno Trulli, Ralf Schumacher, Antônio Pizzonia and Jenson Button.
Räikkönen would have had a chance of winning with a one-stop strategy, but a deflated tyre forced him to make a second pit stop.
Rubens Barrichello also had the same problem later in the day, and Montoya was lucky to finish in the lead, as his left rear tyre began to cut with several laps remaining.
Alonso extended his lead over Räikkönen in the Drivers' Championship to 27 points, 103 to 76, with Michael Schumacher third on 55 and Montoya fourth on 50.
Renault retained an eight-point lead over McLaren-Mercedes in the Constructors' Championship, 144 to 136, Ferrari remaining in third on 86 and Toyota fourth on 78.