Paul Cook's Chesterfield, who are gunning for back-to-back promotions, started the day sixth and just a point ahead of Rochdale, Barnsley and Peterborough United.
Yeovil, who headed into the match with just one win in 10, threatened an upset as James Hayter's cool finish and a low effort from Sam Foley had them 2-0 up by the 57th minute at Huish Park.
However, Chesterfield roared back with a three-goal blitz in the space of 10 minutes, Sam Hird starting the comeback in the 59th minute before two great strikes from Jay O'Shea completed the turnaround and struck another blow to Yeovil's slim survival hopes.
And on-loan striker Jermaine Beckford's fierce drive through the legs of Josh Lillis in the 36th minute was enough for Simon Grayson's men to win 1-0 at Deepdale and move seven points clear of Swindon - albeit having played two games more.
Like Rochdale, Peterborough's play-off hopes took a blow in a 2-0 defeat at Scunthorpe United – who are now 17th and three points clear of the relegation zone.
Leaders Bristol City suffered a rare blip in a 1-1 draw at Oldham Athletic, Carl Winchester's goal in the 75th minute coming just four minutes after Aaron Wilbraham's opener.
Notts County remain in the bottom four after a goalless draw at Walsall, and Fleetwood Town were 1-0 winners at Gillingham.
