Hayter crashed the ball home from close range after 81 minutes to confirm all three points for Gary Johnson's side, who had taken the lead through Sam Foley in the 53rd minute.
Yeovil lost Dan Burn to a second yellow card in stoppage time but by then the game was all over with the visitor's faint hopes of automatic promotion still intact.
Kevin Dawson had a 24th-minute tap-in ruled offside for the Glovers after Steve Arnold had parried a close-range header from Hayter.
Dani Lopez saw a 35th-minute header, which was destined for the top left-hand corner, saved by a diving Marek Stech after the Spanish striker was picked out in the box by Lucas Akins.
Foley curled the ball into the top left corner of the net after the 26-year-old midfielder was found unmarked by Hayter on the edge of the box.
Hayter thumped in his 15th league goal of the season from six yards out to double Yeovil's lead with nine minutes remaining after the Boro defence failed to clear a cross from Foley.
- Sports & Recreation
- Sam Foley