Boro came into this match on the back of three straight defeats but Zoko's 16th goal of the season means they are now six points adrift of their opponents with two games in hand.
Stevenage got off to the perfect start when Zoko did well to control a ball into the box and go past Mark Ellis before finishing with aplomb in the fifth minute.
Crewe came close to equalising, however, when Byron Moore whipped in a great cross from the right with Chuks Aneke's header at the near post going narrowly wide.
Aneke was closer still just before half-time when Moore picked him out again and Stevenage goalkeeper Chris Day was very fortunate as he flapped the ball against his own crossbar.
The Railwaymen continued to press in the second half but the nearest they came to a point was when Mathias Pogba headed over yet another cross by Moore.