Nathan Smith had a header well saved early on, while Shaun Harrad also went close for the Gulls.
Smith broke the deadlock when he headed in Dan Butler's second-half corner.
And substitute Iffy Allen tapped in number two from a Butler cross shortly after coming on.
Torquay are now level on points with Welling, with both sides seven points from safety.
Torquay United claimed back-to-back league wins for the first time this season as they beat fellow strugglers Welling to move off the foot of the National League.