Cech fired home from the edge of the box to deny Ireland the victory which would have taken them into Wednesday's clash in the Czech Republic with high hopes of securing one of the two qualifying positions in Group D.
It looked like Kevin Doyle's wonder goal from fully 30 yards had wrapped up the points for the visitors until Cech's late strike which now means that anything less than a victory in Prague will all but end Ireland's chances of qualification.
Stephen Ireland had given the Irish a great start with the opening goal in the seventh minute but the Slovakians, who had started nervously, equalised before the break through Maros Klimpl.
Shay Given and Lee Carsley returned to the Irish line-up having missed last month's 4-0 friendly win in Denmark.
Steve Staunton brought in John O'Shea and Stephen Kelly at full-back and preferred to give Kevin Kilbane a midfield role, with Charlton's Andy Reid dropped to the bench.
The Slovaks threatened early on when Matej Krajcik narrowly failed to send Filip Holosko clear into the right side of the Republic box.
But the Republic made a dream start in the seventh minute when Ireland maintained his superb international scoring record with the early goal his side craved.
Kilbane crossed low from the left and Robbie Keane - without a goal in seven years of away qualifying matches - unselfishly stepped over the ball to allow Ireland to blast home from point blank range.
It was Ireland's fourth goal in five starts for his country and underlined the reason why Staunton preferred the Manchester City man to the in-form Reid in the middle.
Ireland almost sent Kilbane through in the 19th minute but Slovak keeper Stefan Senecky just managed to gather the ball under pressure on the edge of his box.
Staunton's men continued to look likely to extend their lead with the superb Kilbane consistently causing problems down the left flank.
Former Blackburn man Vratislav Gresko flung in a dangerous cross after 20 minutes which had Richard Dunne frantically back-pedalling in order to clear but the Republic retained control and Ireland curled a low shot just the wrong side of Senecky's left hand post.
If there was any danger of the Irish becoming complacent it was ended just past the half-hour when a strong spell of pressure by the Slovaks turned the course of the match on its head.
Marek Sapara's powerful long-range drive was parried by Given, then moments later a cross by the same player found the head of Holosko in front of goal. But the striker did not get enough contact to steer the ball into the net.
Given turned a long-range shot from Hamsik over the bar before the unrelenting Slovak pressure finally brought an equaliser in the 37th minute.
Jan Durica flicked on a deep corner from the left to leave Klimpl the simplest of chances to head home at the far post.
Suddenly Ireland's early momentum had vanished and the home side, who needed a win to retain any hopes of qualification themselves visibly grew in confidence.
Paul McShane produced a superb saving challenge to deny Holosko a shot on goal in the box in the 49th minute as the home side threatened to continue in the second half as they had finished the first.
Hamsik looped a long range effort into Given's arms before O'Shea's delightful lob set up a rare Republic chance, with Ireland's powerful drive acrobatically saved by Senecky.
The Slovaks should have taken the lead in the 55th minute. Krajcik found space down the right flank and launched a cross from which Marek Mintal fired a diving header inches wide of target.
But the Irish took back the lead out of nowhere two minutes later when Doyle unleashed an unstoppable left-foot shot from 30 yards which rocketed into the back of the net and sent the Irish fans wild.
It was Doyle's fourth goal for his country and he is unlikely score a better one.
Given reacted well to save a Gresko header in the 63rd minute but McShane almost bundled home a third for the Irish.
Staunton introduced Darron Gibson for his competitive debut as his side sought to hang on to a result which would send them to Prague in good heart.
And it was the visitors who looked like finishing the match stronger, with O'Shea seeing his cross booted away from the danger zone then Keane denied a shooting chance by some alert goalkeeping by Senecky.
But as the stadium clock showed 90 minutes the Irish needed a superb challenge from Dunne to prevent Mintal from having an easy chance.
And Ireland were denied victory in heartbreaking fashion when they failed to clear their lines deep into injury time and Cech grabbed a dramatic equaliser.