The striker glanced home Damien Duff's 83rd-minute cross to claim his 40th senior international goal and three precious points, just as it looked as though Ireland would have to settle for a fourth successive draw on the road.
Keane's winner came as news of victories for Group Eight leaders Italy and third-placed Bulgaria filtered through, and will send the Republic into their remaining games - against the Italians and Montenegro at Croke Park next month - knowing second place is there for the taking, and top spot is not beyond them.
Ireland have played a game more than both the reigning world champions and the Bulgarians, but remain just a point adrift of the former and five ahead of the latter.
Giovanni Trapattoni's men were in front within five minutes in Nicosia when Kevin Doyle fired home a fifth-minute opener, but Marios Elia levelled after 30 minutes after Shay Given had pulled off a fine save to deny Ioannis Okkas.
Ireland had chances to win the game before Keane did just that - goalkeeper Sofronis Avgousti denied Glenn Whelan with a superb 50th-minute stop - but they were made to work hard for a win which had the travelling fans inside the GSP Stadium dreaming of South Africa as they departed.
Ireland could hardly have got off to a better start as they forced Cyprus on to the back foot, just at they had done at Croke Park in October last year.
Full-back Andreas Avraam had little option but to concede a fifth-minute corner as Doyle closed on Duff's cross, and the visitors took full advantage.
John O'Shea met Stephen Hunt's cross beyond the far post and headed it back into the mix, and after Keith Andrews' shot had been blocked, Doyle turned and smashed the loose ball past Avgousti.
The lead might have lasted just two minutes, however, had in not been for Given's athleticism, the Manchester City goalkeeper arching his back to claw away Okkas' goal-bound header, earning the good fortune which came his way when Chrysostomos Michail completely miskicked as the ball was fed back across.
It was dangerman Efstathios Aloneftis who had provided Okkas with his chance, and while he was kept quiet for much of the first half by O'Shea and Hunt, when he did get himself into the game down the left, things happened for Cyprus.
The equaliser duly arrived from that flank with half an hour gone when, after Dunne had dispossessed Okkas inside the penalty area and Sean St Ledger had blocked Avraam's shot, Elia made no mistake to lash the ball into the far corner.
Ireland's response was swift and concerted, and they might have regained the lead had Andrews' 36th-minute effort from distance been a foot closer to Avgousti's right post or had Kevin Kilbane been able to keep his header a fraction lower seconds later.
Konstantinos Charalambides headed over at the other end five minutes before the break, but Trapattoni's men left the pitch at half-time knowing the game was very much there for them to win.
Just as they had done in the first half, Ireland started strongly in the second, and might have been back in front twice within the opening five minutes.
First Hunt headed a Duff cross into the side-netting from an acute angle, and then Whelan forced Avgousti into a top-class save with 50 minutes gone.
Keane's knock-down from Doyle's cross fell perfectly for the Stoke midfielder, who struck it first-time towards the top corner, only for the goalkeeper just to get his fingertips to it.
There was an anxious moment for the visitors, however, with 61 minutes gone when Okkas looked to have got marginally the better of Dunne as the pair raced into the box shoulder to shoulder and the striker ended up on the floor.
But Austrian referee Thomas Einwaller was not impressed, much to the annoyance of the locals.
Trapattoni replaced Hunt with Aiden McGeady with 23 minutes remaining, although the winger's first contribution was to concede a corner from which Charalambides should have done better.
Cyprus substitute Nektarios Alexandrou carved his way into the Republic's penalty area within a minute of his arrival and might have caused serious damage had O'Shea, who looped a header just over seconds later at the other end, not intervened in the nick of time.
But it was left to Keane to do what he has done so often in the past, beating Avgousti to Duff's 83rd-minute cross to glance a header home and send the travelling fans into raptures.