Exeter edged closer to the Blue Square Premier play-off zone thanks to Richard Logan's second-half strike.
Both sides went close in the first half, with Adam Stansfield's header for the hosts just wide and Simon Heslop forcing Andy Marriott into a fine save.
After the break, Matthew Taylor put Logan through and, from six yards, he found the bottom corner.
Lewis Killeen came close to equalising but his close-range shot rebounded back off defender Daniel Seabourne.
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