Two-time defending Formula One champion Fernando Alonso of McLaren was third.
Overall leader Lewis Hamilton of McLaren had been in third place but dropped to fifth after shredding a tire on the 43rd lap. Nick Heidfeld was fourth.
At the end of the 58-lap race, Massa was 2.2 seconds ahead of Raikkonen, with Alonso 26 seconds back. Hamilton was 45 seconds behind Massa.
With five races left, Alonso gained on his teammate after being as low as sixth in the early stages of the race.
In the overall standings, Hamilton's lead was cut to five points over Alonso, 84-79. Massa is third with 69 points and Raikkonen is next with 68.
The Ferraris and McLarens continue to divide the races. In the 12 races so far, Alonso, Hamilton Massa and Raikkonen have won three each.
Massa made a reversal after his last race. He finished 13th in the Hungarian GP on Aug. 5 after a disappointing qualifying run that made him start from the back of the grid.
"Three Grands Prix here, two wins. Can't be better," Massa said. "Starting from pole, good car, difficult race. I managed to keep my concentration."
At the start Sunday, the two Ferrari drivers went to the top positions with Hamilton third. Alonso was beaten to the first turn by the two BMW-Sauber drivers and was sixth after the first lap. After five laps, he was more than seven seconds from first and, more important, almost five behind Hamilton.
"If someone told me on lap two you would be on the podium ... I would be very happy," Alonso said. "At the end, the final result is the best thing of the weekend."
Alonso was penalized five spots on the starting grid for the Hungarian GP after delaying his teammate in the pits in the final minutes of qualifying, although Hamilton refused to let Alonso pass him earlier, contrary to McLaren team orders. Hamilton won and Alonso was fourth.
At 10 laps Sunday it was still the two Ferraris ahead of Hamilton, with Alonso about 10 seconds back. Alonso was able to move into fourth past Heidfeld and Robert Kubica at the first pit stop, but he was still losing time.
Raikkonen closed to within a second.
"I made a small, small mistake and Kimi closed the gap," Massa said. "Just a small mistake made my life difficult."
Raikkonen said the result was predictable after Saturday when Massa was first, two places ahead of the Finnish driver.
"In Formula One these days the race is pretty much decided after qualifying," Raikkonen said.
Things changed on the 43rd lap when Hamilton was flapping rubber from his shredded front tire while in third place. Hamilton managed to make it to the pits to change the tire but Alonso moved into third and Heidfeld was fourth.
"I saw some bits fly off the tire," Hamilton said. "It was lucky I didn't put the car in the gravel and managed to control it back to the pits as this meant that in the end I only lost two places."
Hamilton said the tire cost him a place on the podium.
"I was pushing obviously. Without a doubt we would have finished third. I still had six laps more fuel than the Ferraris. I was hoping in those six laps I could get Kimi," Hamilton said.
"Then the tire went."
Renault's Heikki Kovalainen was sixth, followed by Nico Rosberg of Williams and Kubica.
The next race is the Italian Grand Prix on Sept. 9, followed by the Belgian Grand Prix a week later.
