The 31-year-old LA Galaxy striker, who missed a penalty in the reverse fixture in October, headed wide from just five yards with 16 minutes of a distinctly uncomfortable contest against Slovakia remaining to let slip a victory his side never really deserved.
Substitute Simon Cox was similarly wasteful after being set up by Keane six minutes from time as the Republic conceded two points to Russia in the race to top Group B.
Ireland head for Moscow on Tuesday night knowing victory is essential if they are to pip the Russians, who had beaten Macedonia 1-0 earlier in the evening, to automatic qualification.
Ten years and a day since their famous World Cup qualifier win over Holland, Giovanni Trapattoni's side only really threatened to take the game by the scruff of the neck in a frenetic conclusion.
Up until that point, the Slovakians had handled them with little difficulty and might have claimed all three points had it not been for keeper Shay Given.
A record sixth successive clean sheet was little consolation to Trapattoni's men as a must-win game yielded only a point, and their dejection was clear as they trudged off the pitch at the Aviva Stadium with boos ringing in their ears.
Slovakia left Dublin by far the happier, and Ireland could yet find themselves in third place in the group on Tuesday night if Vladimir Weiss' side better their result when they face Armenia in Zilina.
Ireland headed into the game brimming with confidence on the back of a five-game unbeaten run and looking to lay the foundation for victory with another shut-out.
They reached half-time with 50% of that mission completed, but having shown little sign of the form which accounted for Macedonia in Skopje and then Italy in Liege in June.
Having drawn 1-1 in Slovakia, they knew Weiss' men would be no push-over, and just how much of a threat the visitors represented quickly became clear.
Ireland were disjointed to say the least, and as Slovakia grew in confidence, it was they who looked the more likely to open the scoring.
Given was grateful to see Vladimir Weiss Junior, the manager's son, fire straight at him with 19 minutes gone, and the Aston Villa man had to get down well to his left nine minutes later to claw Filip Holosko's header out of the bottom corner.
Trapattoni's suspicion that Slovakian playmaker Marek Hamsik would start despite being rated at only 50-50 with a knee injury on the eve of the game proved correct.
He linked repeatedly with Juraj Kucka behind him and Miroslav Stoch and Holosko ahead of him, and as full-backs Peter Pekarik and Marek Cech exploited the space behind opposite numbers Stephen Ward and John O'Shea, Ireland found themselves stretched.
But for all that, it was they who created the best opening of the half, although they had to wait until the 38th minute to do so.
Damien Duff came off the right wing to play a one-two with Keith Andrews and continued his run into the box to receive the return pass.
Duff's left-foot shot clipped Martin Skrtel on its way to goal, but the deflection failed to wrong-foot keeper Jan Mucha, who managed to beat it away.
Ireland returned after the break no doubt having been told in no uncertain terms that they would have to be much better in the second half, and they resumed in determined fashion.
Both sides had penalty appeals correctly waved away by Portuguese referee Pedro Proenca inside the opening four minutes after Weiss went down under Aiden McGeady's challenge and then Glenn Whelan collided with Pekarik at the other end.
Duff fired over the angle of bar and post with 58 minutes gone, but his side would have been behind three minutes later had Sean St Ledger not blocked Hamsik's goal-bound shot with his chest after Holosko had got in behind Richard Dunne and teed up his captain.
Trapattoni introduced Cox as a 64th-minute replacement for Kevin Doyle, but with Weiss terrorising the home defence, Given was seeing far more of the ball than Mucha.
However, the chance of which Keane would have dreamt last night finally arrived with 16 minutes remaining when Duff curled in the perfect cross from the right wing.
Keane met the ball with a firm header just five yards out, but somehow powered his effort wide with Mucha hopelessly exposed.
Cox might have spared Keane's blushes six minutes from time when he ran on to the former Tottenham frontman's lay-off, but he dragged his shot wide of the post.