The teams were level at 1-1 with five minutes remaining but there was an incredible change of fortunes for Spurs in that time.
News had filtered through that QPR were winning at West Ham and therefore Spurs would slip into the relegation zone of the Southern Division.
However, West Ham equalised and that sparked a late rally that saw Bianca Baptiste and new signing Irene Martin Garcia both go close before the thrilling finale.
Amy Cooper took a quick free-kick centrally, Robyn McEvoy and Irene then combined to play in Sam Pittuck who instead of shooting found Andra - on as substitute just 15 minutes earlier - who finished in style for 2-1.
The result means Spurs leapfrogged over QPR and Lewes into eighth place of 10.
Manager Juan Amoros admitted it was a game his team could not afford to lose, even though Brighton are flying high and scrapping with West Ham for third.
The ladies went into the game without top scorer Wendy Martin but were boosted by the arrival and debut of Irene, a Spanish Super League winner with Rayo Vallecano.
Brighton went close with an early free-kick but Spurs took the lead with a fantastic goal from Mollie Kmita, who controlled Robyn McEvoy's cross before volleying home.
The visitors started the second half strongly and forced Jo Ayre into a fine save from Lily Agg before equalising through Kim Stenning, who appeared in an offside position, but the goal stood.
At that point, things looked tough on the ladies but they recovered to find that vital winning goal in the last minute.
"After two matches where we'd lost points in the last minute, we thoroughly deserved this," said Juan.
"The girls merited the victory and worked for it from the first until the last minute of the game. Moments like this make you love football!
"Now we have to think about Yeovil, our next match and we cannot relax despite these three important points."
The ladies take on mid-table Yeovil in the FAWPL Southern Division at Harlow Town FC on Sunday, kick-off 2pm.
Spurs Ladies v Brighton: Ayre, O'Halloran (Albertsen, 65), Schillaci, Lane, Downie, Cooper, McEvoy, Martin Garcia, Pittuck, M Kmita (Marcoci, 75), Baptiste (R Kmita, 85). Unused subs: Heath, Picton.