Giovanni Trapattoni's men looked set for an embarrassing defeat when Kairat Nurdauletov glanced home after an insipid first-half performance from the visitors.
Kazakhstan, ranked 116 places below the Republic, controlled almost all the second half until Keane scored from the penalty spot after 87 minutes and Doyle blasted home in the dying seconds to hand the beleaguered Trapattoni a much-needed three points.
Until the final five minutes of this game it appeared the Emerald Isle were set to stoop to a new low under Trapattoni, who had come under fire for the country's poor UEFA EURO 2012 campaign, and a number of off-field issues that have since followed.
Trapattoni promised that this game would be the start of a new promising era, but for the majority of it his team were easily taken apart by Kazakhstan. The eastern European nation did play well inside the half-empty Astana Arena, but their previous record in qualifiers is abysmal, and had it not been for a questionable penalty, and for a bit of quick thinking from substitute Doyle, this could have been the final nail in the Trapattoni's management of this team.
There was no indication that the Republic were going to put on such a first-half horror show in the opening minutes as they started strongly. James McCarthy, making his first competitive start, saw his low curling shot tipped wide and John O'Shea's deflected header just missed the target.
The Kazakhs started to settle in to their rhythm, however, and threatened through Tanat Nusserbayev. The FC Astana forward drove at the Republic defence, but his threaded pass to Alexandr Kirov went to waste after the full-back mis-timed his run. Panic spread in the Republic defence moments later when a cross trickled through to the back post where Ulan Konysbayev was lurking, but Keiren Westwood sprang off his line to the rescue.
The Republic were struggling to make any impact on the game and often resorted to lumping the ball to Jon Walters - a tactic that failed almost every time. The one time the Stoke man did look effective in the first half was when he played a neat one-two with Simon Cox, but the Nottingham Forest player, playing out of position on the wing, fired in to the side-netting.
Keane had a quiet first half, with his only contribution of note a darting run which led to a penalty appeal that was turned down after a challenge by Mikhail Rozkhov. The 300 travelling fans bellowed at their team, but they did very little, with Sean St Ledger's weak header summing up the visitors' limp first-half performance.
The opening goal that had been coming for a while arrived nine minutes before half-time when Genrikh Shmidtgal swung in a wicked corner and Nurdauletov glanced home from ten yards. It was almost 2-0 moments later. Westwood parried Konysbayev's shot in to the path of Nusserbayev but he could only hit a post.
Despite their sub-par performance in the opening 45 minutes, Trapattoni did not make any changes at half-time. Worryingly for the Italian, the Kazakhs remained on top. Shmidtgal probed the Republic defence with a foraging run and Nusserbayev powered a volley over the bar as the away side struggled to get in to the game.
Trapattoni finally made a change just before the hour when the ineffective Cox was replaced by Doyle. The Wolves man scurried straight in to the box and went down under a challenge, but his penalty appeal fell on deaf ears.
The Italian boss nervously checked his watch on the touchline as his team kept failing to trouble the hosts. Nusserbayev fired a low shot just wide of Westwood's goal before being substituted to a standing ovation from the home crowd.
Glenn Whelan tried a long shot that summed up the Republic's desperation as the clock ticked on with no equaliser. Baurzhan Jolchiyev managed to wrestle his way through a dormant Republic back four, but Westwood pulled off a terrific save to deny the substitute what surely would have been the winning goal.
The away side plugged away and were handed a way back in to the tie three minutes from time when Keane was bundled over in the box by Rozhkov and the referee pointed to the spot. The former Tottenham striker showed nerves of steel to calmly dispatch the spot-kick to the Kazakh keeper's right.
The Republic completed their stunning comeback in the final minute when Doyle latched on to Stephen Ward's knock-down and volleyed home from close range.