The German started the race in second place behind Lewis Hamilton, but by the time that the second lap was underway, he had gone beyond the Mercedes driver and into first spot.
"It was a fantastic race for us from start to finish. It was very good tactics and it helped to get past Lewis on the first lap. We were a bit afraid of the rain coming but it was a great race," he told reporters.
The result marked the second time that Vettel had taken the chequered flag in Belgium.