Dyer struck after 25 minutes when he latched onto Steve Howard's flick and rounded full-back Terrell Forbes before firing an angled low shot into the far corner.
Matty Fryatt almost gave the Foxes a sixth-minute lead when he turned and drove just wide after Howard had headed on Paul Henderson's long clearance.
Matt Oakley spurned a fine chance just before the break when he brilliantly controlled Andy King's pass into the box but then blasted wide from 14 yards with just the goalkeeper to beat.
Yeovil keeper Josh Wagenaar kept City at bay 20 minutes from time when he parried Fryatt's 18-yard drive and then recovered quickly to beat away Dyer's follow-up shot.
The Glovers' best chance saw an unmarked Aidan Downes head Danny Schofield's left-wing cross into the side netting but City were good value for the points.