Goals from Robyn McEvoy and a belter from Irene Martin secured the points to lift Spurs to eighth of 10 in the FAWPL South, level on points with Colchester in ninth and seventh-placed Gillingham.
The bottom two teams face relegation. Lewes are just a point ahead in sixth after winning successive matches against QPR and Yeovil.
With two games remaining against rivals Gillingham and Colchester, it's all set for a nerve-wracking end to the campaign.
Spurs were determined from the first whistle against QPR and Robyn opened the scoring in the fifth minute, winning possession from the Rangers' centre-back and flicking home.
Jo Ayre did well to smother Elly Maggs' effort from a corner but Bianca Baptiste then went close at the other end and Irene's blast was superbly saved by QPR goalkeeper Sophie Cheadle.
Spurs held the territorial advantage in the second half and victory was secured in style when Irene let fly from fully 30 yards, the ball arrowing into the top corner.
Sam Pittuck almost made it three late on but was denied by Cheadle.
Manager, Juan Amoras, said: "This was a crucial game for us and we dominated it from the first minute. I just can say thank you to the girls for their effort and we're now thinking about the two crucial remaining games against Colchester and Gillingham."
The first of those games is at Gillingham on Sunday, kick-off 2pm.
Spurs: Ayre, O'Halloran, Schillaci, Downie, Lane, Cooper, Pittuck, Martin (R Kmita, 85), Baptiste, Marcoci (Heath, 90), McEvoy. Unused subs: Cheeseman, M Kmita, Waters.