Barnet moved up to fifth after exposing Wrexham's defensive frailties.
Liam Hatch opened the scoring on 58 minutes when he was left unmarked inside Wrexham's six-yard box to tap in Jason Puncheon's low cross.
The striker, who hit the bar in a dire first half, doubled the lead 10 minutes later when he benefited from a howler from home goalkeeper Michael Jones.
Eifion Williams almost pulled a goal back after a goalmouth scramble and then had a penalty shout turned down.