Gateshead, who lost in last season's playoff final, opened the scoring on 18 minutes when Lewis Guy got ahead of his marker to head home from close range.
The home side continued to dominate and just after the half-hour mark, they made it 2-0 when Maddison struck a left-footed effort into the roof of the net.
Torquay, who were relegated from League Two in the previous campaign, returned for the second half with greater attacking intent, but they were unable to reduce the deficit thanks to Gateshead stopper Adam Bartlett.
Louis Briscoe also went close for the visitors, but with 16 minutes remaining, Maddison wrapped up the points for Gateshead with another venomous hit from the edge of the penalty area.
Gateshead continued to push for a fourth goal, but that saw them undone in defence as Briscoe netted a consolation goal for Torquay in the final minute of the match.