Winston Reid scored in injury time to give New Zealand their first-ever point of the World Cup - and send the All Whites level in Group F with World Champions Italy.
Slovakia's Robert Vittek had struck early in the second half to leave his country in control but Reid had other ideas as he got on the end of Shane Smeltz's cross.
Vittek headed past New Zealand goalkeeper Mark Paston at the beginning of the second half, after the Kiwis had kept their much-more fancied opponents at bay for the first 45 minutes.
In a game short on quality New Zealand adopted a back-to-basics direct approach from the off, crowding the midfield to keep the Slovakians quiet.
But the All Whites - in their first World Cup for 28 years - had enjoyed chances of their own, with Chris Killen and Shane Smeltz going close for Ricki Herbert's side.
And after Reid had denied Vittek a second midway through the second half, he headed home to leave it all to play for in Group F.
After a cagey start from both sides, Killen enjoyed the first chance of the match in the fourth minute, but the New Zealander's chip went over the bar.
Two minutes later Killen should have done better with his header off Simon Elliott's free kick, but the Middlesbrough forward could only nod towards Slovakia keeper Jan Mucha.
Slovakia looked content to sit back and hit New Zealand on the break, but were dangerous in their first meaningful venture forward, in the 28th minute.
Vladimir Weiss - son of Slovakia coach Vladimir Sr - put through for Stanislav Sestak, who could only fire wide under pressure from Kiwi captain Ryan Nelsen.
New Zealand 'keeper Paston had a huge let-off in the 33rd minute when he horribly miscued a clearance to concede possession to Robert Vittek, but he recovered in time to block the striker's shot.
Smeltz came close to breaking the deadlock six minutes from half-time after some good play by All Whites team-mate Rory Fallon, but Slovak keeper Mucha managed to palm the ball clear.
Paston was on hand on the stroke of half-time to tap captain Marek Hamsik's 20-yard shot over the bar, as Slovakia began to show their quality.
And four minutes after the restart Vittek made the breakthrough, beating Reid - and avoiding an offside flag - to head Sestak's cross past Paston.
The goal sent New Zealand into their shells and an unmarked Hamsik blew a chance to double Slovakia's lead on 64 minutes when he blasted high over the bar from the edge of the box.
Vittek could also have made it two on 70 minutes but for Reid's brave last-ditch tackle in the penalty box, after Hamsik had carried the ball up on the break from Slovakia's own area.
NEW ZEALAND (3-4-3): Paston; Reid, Nelsen, Vicelich (Christie 78); Smith, Bertos, Elliott, Lochhead; Fallon, Smeltz, Killen (Wood 72)
Subs: Moss, Sigmund, Brown, Barron, McGlinchey, Clapham, Mulligan, Boyens, Brockie, Bannatyne.
SLOVAKIA (4-4-2): Mucha; Zabavnik, Durica, Skrtel, Cech; Weiss (Kucka 90), Strba, Sestak (Holosko 81), Hamsik; Vittek (Stoch 84), Jendrisek
Subs: Pernis, Pekarik, Kozak, Sapara, Jakubko, Kopunek, Salata, Petras, Kuciak