With the referee's whistle poised to blow, Kathryn Fudge fired in to secure the tightest of wins 27-26.
It could have gone either way throughout the match with the sides level at 15-15 at half time.
Seven goals from Kelsi Fairbrother (pictured) underpinned Great Britain's victory, although the team played much better than in their opening day loss to Austria on Wednesday.
"Slovakia were the top seeds going into this competition, and although they aren't as strong as many people thought this is still a good win and a great day for British handball," said head coach Jesper Holmris.
"Everybody played well, and our defence was better than yesterday.
"What is great about this win is that everything that went wrong against Austria we corrected.
"We're looking forward to playing Cyprus and Poland in our final two matches now."
December 2010: GB handball team couldn't Asker for more