Both sides appeared to be still suffering from a New Year's Day hangover as they produced a dour display that looked set to finish all square until Yeo's late intervention.
A scrappy opening period saw little of note with both sides resorting largely to long ball tactics.
A swift break upfield by Kevin Ellison saw him play in Michael Branch, but the striker appeared to loose his footing at the vital moment and his shot was weak and easily gathered by Red Imps keeper Alan Marriott.
The restart saw Ellison test Marriott with a long-range effort that the keeper tipped over at full stretch.
The Chester midfielder looked the most likely player to break the deadlock and he hit two further sweetly-struck efforts that Marriott was well-positioned to save.
Substitute Yeo was thrown into the fray just after the hour mark and he had a chance to secure the points but hit a left-foot drive that flew just passed the post.
Chester failed to heed to warning as the striker hit a powerful effort deep in stoppage time that Chris MacKenzie in the City goal was unable to stop despite getting a touch to it.