It was the ninth win of Alonso's F1 career.
"Thanks to the mechanics for a perfect stop," he said. "This was a fun race."
With five laps remaining, Schumacher, the pole-sitter, was close enough to make a tentative move to the inside of Alonso at the end of the straight, but couldn't make the pass.
"If you think where we had been last year, if you see what has happened over the winter time and somebody would have told us we would finish second we would be absolutely happy about it," Schumacher said.
Kimi Raikkonen, Jensen Button and Juan Montoya were 3-5.
The next race is the Malaysian Grand Prix on March 19th.