Johnny Mullins put the visitors ahead after 24 minutes of Saturday's League One clash at Huish Park, before County found themselves 2-1 down as Yeovil hit back through Nathan Smith and Paul Warne.
But further goals from Tommy Rowe, Mullins and Carl Baker put the game beyond the struggling home side.
Right-back Mullins opened the scoring with his first of the afternoon with a 20-yard right-footed effort after 24 minutes.
The Glovers, however, were behind for barely two minutes as Smith beat County goalkeeper Owain fon Williams from fully 30 yards and then Warne struck from a similar distance after 43 minutes.
Rowe immediately equalised in first-half stoppage time from the edge of the penalty area before Mullins weaved his way past Nathan Smith to score his second goal with a low, left-footed strike. Substitute Baker added Stockport's fourth two minutes from time with a fine header from Michael Rose's centre.