The Robins had dominated long spells of the game and created numerous chances, but looked set to succumb to Jake Robinson's 55th minute strike for the visitors.
However, a desperate spell of good old route one football in the closing moments earned Cheltenham three more vital points in their fight against the drop.
Cheltenham had the best of the first half chances with powerful striker Steve Brooker - a loan signing from Bristol City - making his presence felt.
Brooker saw an early shot saved by Brighton goalkeeper Michels Kuipers, then sent a drive just wide and flashed a header inches over the bar.
His strike partner Steven Gillespie also had two shots saved by Kuipers and there were penalty appeals turned away on two occasions when first Michael D'Agostino and then Brooker felt they had been impeded in the box.
Cheltenham began the second half in the same positive fashion, but they were undone 20 minutes after the restart when Matt Richards made his way up the flank from left-back and played a pass inside to Glenn Murray.
He chested to Dean Cox, who found Robinson in space on the right-hand side of the area and his low drive beat goalkeeper Shane Higgs from 15 yards.
Cheltenham went close with a 30-yarder from Alex Russell that Kuipers flew to save and a Gavin Caines header that was cleared off the line before the drama began.
Manager Keith Downing cast his final throw of the dice by sending on winger Ashley Vincent and striker Paul Connor, and it was the latter who suddenly started winning everything in the air.
The board showing four minutes of added time had just been shown when a long clearance from Higgs was flicked on by Connor and Russell directed a deft lob shot over Kuipers for the equaliser.
Then two minutes later came an almost carbon copy build-up.
Another Higgs clearance and Connor flick this time resulted in Gillespie rounding Kuipers and scoring into the empty net to blow the roof off Whaddon Road.