Although they created the two best chances of the match in the final 20 minutes, Giovanni Trapattoni's side were void of finesse in the final third of the pitch and were lucky to escape with a draw.
Ireland travel to Moscow on Tuesday ahead of Slovakia in the group by way of a better head-to-head record. Their rivals could move ahead after they host Armenia next week but face Dick Advocaat's Russian side in their penultimate game on October 7.
"In the group, everything is open. We must just now win against Armenia on Tuesday. I hope Ireland have the same result as they had today in Moscow and then everything is possible," Slovakia coach Vladimir Weiss told a news conference.
"It is not important just now [that Ireland are ahead in the group]. We can see after the last game."
The hosts dominated the opening exchanges but were unable to carve out an opportunity and the first chance of the game fell to winger Vladimir Weiss, the coach's namesake son, who fired straight at goalkeeper Shay Given from inside the box.
Once they had settled, the Slovakians began to look the far more dangerous side and Besiktas striker Filip Holosko forced Given to palm his header past the post a few minutes later.
Ireland's play turned scrappier but following a neat one-two with Keith Andrews, Damien Duff made Slovakia goalkeeper Jan Mucha work for the first time with a deflected shot from close-range.
The game opened up in the second half and the visitors began to look every inch the side who knocked out Italy en route to the second round of last year's World Cup.
They could have led on the hour had defender Sean St Ledger, whose later booking rules him out of Ireland's next game, not brilliantly blocked Marek Hamsik's goal-bound effort.
The most clearcut chance of the match fell the way of Ireland but LA Galaxy new boy Robbie Keane, who missed a penalty when the sides drew 1-1 in Zilina last year, somehow managed to head over when unmarked from four metres out.
Aston Villa defender Richard Dunne was presented with a similar opportunity in injury-time but again headed over before his side were booed off the pitch by the home fans.
"I am a little bit disappointed because I think we had three big opportunities and usually it's possible to score one goal from that," Trapattoni said, adding a Simon Cox half-chance late on to the list of chances.
"I think we must think it's possible to win in Russia. Why not?" the Italian added.
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