BAR-Honda driver Jenson Button finished second after starting from pole position with Juan Pablo Montoya third in a Williams-BMW The bottom 6 teams in the 2003 Constructors' Championship were entitled to run a third car in free practice on Friday.
The 2004 San Marino Grand Prix marked the 10th anniversary of Roland Ratzenberger and Ayrton Senna's fatal accidents in 1994.
Both Giancarlo Fisichella and Kimi Räikkönen failed to set a time in the session, leaving them at the back of the grid.
Rain fell on the Imola circuit overnight, washing away much of the rubber that had been laid down over the weekend, theoretically handing the advantage to teams with Bridgestone tyres.
Jarno Trulli, momentarily in second place, pitted on lap 12, with fast work by the Renault team allowing him to take 4th position from Ralf Schumacher.
Soon later he retired from the race, citing a continuously locking rear brake, which made the car difficult to drive.
da Matta was served with a drive-through penalty for ignoring blue flags, but made a mistake and went off track soon after, ending his race.
Sato retired from the race with a spectacular Honda engine failure with 6 laps remaining, possibly causing worry for teammate Button, who was in 2nd position.
Michael Schumacher cruised to the finish line to win his fourth race of the year, with Button in 2nd, and Montoya holding on to the final podium spot ahead of Alonso.
Trulli survived an attack by Barrichello on the final lap to hold on to 5th, with Ralf Schumacher and Räikkönen closing out the pointscorers.
The constructors championship underlined Ferrari's incredible early dominance, with the Italian team on 64, over double the score of second-placed Renault, on 31, followed by both Williams and BAR on 27.