Wrexham fought back from Kyle Perry's 13th-minute strike to rekindle hopes of making the play-offs.
In the process the Dragons ended a run of three draws and two defeats. Matt Jansen's levelled two minutes after Perry hit home.
The visitors then had to wait until the 74th minute to go in front, Nathan Fairhurst's outstanding effort rewarding their patience.
Northwich were the better team for long periods, but were unable to capitalise.
Wrexham boss Dean Saunders: "That's what we needed. It wasn't the best we've ever played and we were all over the place at times.
"Mind you I thought we were playing against the Harlem Globetrotters there. At the end of the game they had four players on there who were about 6ft 7in.
"I've never seen a team that big and the ball was getting lumped forward into our box and there's always a chance for a little flick-on.
"But great goal from Nathan Fairhurst, great goal from Matt Jansen. We scored two at last and you could see after we scored the second one the football was a bit more relaxed."
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