Fullback Reid popped up to glance a header past Jan Mucha that went in off the foot of the post to bring the All Whites level after Robert Vittek had put Slovakia in front five minutes after halftime in what had been a fairly pedestrian contest.
“I think the nation will be in reasonably good spirits tonight,” said modest New Zealand coach Ricki Herbert. “We keep on dreaming. We have a chance like everyone else.”
Asked if it was their best ever achievement he added: “It would have to be. We have never picked up a point at a World Cup. We have thrown some really good punches tonight and got what I thought was an extremely good result”.
Until New Zealand’s late strike Slovakia, making their World Cup debut as an independent nation, had seemed set to top the section ahead of world champions Italy and Paraguay who drew 1-1 in the group opener on Monday.
Vittek scored when he met a diagonal Stanislav Sestak cross with a powerful header from 10 metres after Reid had missed the ball completely in the cold and windy conditions at the Royal Bafokeng stadium.
It was a rare moment of quality in a dreary game during which New Zealand, using a 3-4-3 formation, largely frustrated the cautious Slovaks who appeared reinvigorated after advice at the interval about how to approach the second half.
The Slovaks lifted their tempo and pushed forward more aggressively from then on and gave New Zealand few chances to regain a foothold in the game, their superior technique and movement giving them control of possession.
Slovakia had enjoyed most possession in an opening half littered with errors as the conditions made it difficult for both teams. Few chances were created but New Zealand’s good organisation enabled them to stay in contention.
Chris Killen and Shane Smeltz had chances but shot wide for the All Whites, while Sestak and Vittek did the same at the other end where New Zealand goalkeeper Mark Paston looked shaky. He miskicked once and made other errors of judgement.
A square free kick to Slovakia captain Marek Hamsik, after a foul by Tony Lochhead on Erik Jendrisek, saw the playmaker fire in a 25-yard shot that Paston saved just before the break.
It was one of few bright moments in a tight game in which the Slovaks struggled for a breakthrough until Vittek’s goal.
But just when it seemed they had secured the points Reid struck to help atone for his earlier mistake and it was the New Zealand players who were celebrating at the end.