Danny Wilson's side were behind at the break but the triple salvo leaves Brighton staring relegation to League Two in the face.
There is now a nine-point gap between the teams, although Brighton have a game in hand.
The home team took a flattering lead in an undistinguished first half.
The Swindon defence looked comfortable until the 38th minute when a corner by the influential Dean Cox was headed back towards the near post by Gary Dicker for skipper Adam Virgo to volley in from close range.
Brighton were on course at that stage for back-to-back wins for the first time since November after victory at doomed Hereford but it all went horribly wrong for them after the break.
They were caught cold by a Swindon equaliser in the 47th minute. A free-kick was nodded upwards rather than away by Tommy Elphick and Billy Paynter won the loose ball in the air for Gordon Greer to toe-poke in the volley from two yards.
Brighton were still reeling from that setback when they fell behind three minutes later.
Simon Cox surged through the middle to unleash a fierce shot which keeper Michels Kuipers could only parry and Paynter rammed in the rebound.
Even worse followed for Russell Slade's stunned outfit in the 58th minute when Cox was left unmarked at the near post and he guided in his 28th goal of the season on the volley from Anthony McNamee's cross.
Dicker volleyed in a last-minute consolation for Brighton from substitute Gary Hart's cross but it came too late to rescue the Seagulls and they now look certainties for the drop.