The Grecians only had themselves to blame after some comical defending before the break.
Johnny Allan gave the visitors the lead after a mistake by Scott Hiley before Sean Devine pulled Exeter level. Paul Brayson fired Northwich ahead before a calamitous mistake by goalkeeper Paul Jones resulted in an own goal by Andy Taylor.
Steve Flack's late header proved little more than a consolation for Exeter.
Northwich stunned Exeter when they took the lead in the eighth minute. Hiley failed to control a back pass and the mistake left Allan to race on and stroke the ball past Paul Jones.
The Grecians were level five minutes later when Alex Jeannin's corner was flicked on by Paul Buckle and Devine fired from close range.
But the visitors regained the lead when Brayson stroked home a sublime left-foot strike from the edge of the box after he was picked out by Steve Garvey.
Northwich made it three in the 28th minute in bizarre circumstances.
Jones completely missed his kick from Taylor's back pass and the goalkeeper watched the ball roll into the empty net.
Exeter attempted to respond once more and Kristian Rogers saved well to keep out a free-kick from Taylor and a strike from Flack.
After the break Exeter threw everything at the strugglers and Gary Sawyer had a shot cleared off the line in the opening minutes.
Garvey unleashed a shot from the edge of the box which struck a post for Northwich, who looked dangerous on the break.
A bad afternoon got worse for Exeter when substitute Jake Edwards was sent off for appearing to stamp on Karl Munroe.
In injury-time Flack rose highest to head home Gareth Sheldon's corner but it was too little, too late for Exeter.