Vladimir Weiss' side had the better of the chances but could not make the breakthrough until the 91st minute. By that time they had a man advantage after Vance Sikov had seen red for two bookable offences at Bratislava's Stadion Pasienky.
The first half was a dour affair with chances few and far between.
Holosko's 15th-minute header was comfortably saved by Edin Nuredinovski while Slovakia counterpart Jan Mucha easily dealt with Ivan Trickovski's strike three minutes later.
Marek Hamsik fired over in the 24th minute and then missed the target again 13 minutes later. Miroslav Stoch also failed to test Nuredinovski three minutes before the break as the teams headed into the interval goalless.
Slovakia continued to push after the interval, Vladimir Weiss' dangerous strike saved by Nuredinovski. Hamsik passed up two close-range efforts midway through the second half as the hosts continued to be frustrated.
Home goalkeeper Mucha had to be alert when called upon to keep out a 71st-minute blast from captain Goran Pandev.
Slovakia missed further opportunities through Hamsik and substitutes Juraj Kucka and Erik Jendrisek, but their cause was aided six minutes from time when Sikov was sent off.
The home team committed everyone forward and were soon rewarded when Holosko struck from close range to steal the points.