The Liverpool hitman headed home the 35th goal of his senior international career with just five minutes gone to extend Giovanni Trapattoni's unbeaten run to six games and put his side firmly in the race for top spot in Group Eight.
But it took a superb 86th-minute save from Shay Given to deny Dimitris Christofi an equaliser as Cyprus emerged from a lethargic start to finally make an impression.
Ireland dominated the opening 45 minutes and could have been even further ahead by the break but for a solid display from Cypriot keeper Antonis Giorgallides and the heroics of defender Marios Elia.
Given had to make one vital first-half save from Michalis Konstantinou, but although he was rarely called upon again until the death, the men in front of him were forced to mount a determined rearguard action as the visitors belatedly found their feet.
Cyprus' 5-2 demolition of Ireland in a European Championship qualifier in October 2006 and the 1-1 draw at Croke Park which followed it a year later have burnt deep into the national psyche.
The fact that Angelos Anastasiades' side returned to Dublin with only one point to show for their efforts against Italy and Georgia when they might have emerged with all six, did little to quell the sense of uneasiness ahead of kick-off.
But Trapattoni was handed a boost shortly before kick-off when winger Efstathios Aloneftis, a man he had singled out as a major threat, was forced to withdraw after the warm-up, resolving in an instant the headache over whether to play Paul McShane at right-back or move John O'Shea across.
While all eyes may have been on midfielder Darron Gibson, a controversial replacement for the injured Steven Reid, it was two more established members of the Republic side which set the tone for the night.
Where Cyprus had embarrassed the Irish with their slick inter-play and movement on their last two meetings, wingers Damien Duff and Aiden McGeady took up the challenge of pinning the visitors back inside their own half, and did so to good effect during the opening 45 minutes.
It was they who combined to hand Keane the chance to give his side a dream start with just five minutes gone when the Celtic man picked out his Newcastle counterpart and he supplied the perfect right-foot cross for Keane to head unopposed into the empty net.
But the torment did not end there for a strangely subdued Cyprus team with Duff shooting straight at Giorgallides after 17 minutes and McGeady forcing him to beat away a stinging drive 10 minutes later.
However, it was defender Andreas Constantinou who almost unwittingly doubled Ireland's tally 10 minutes before the break when his attempt to block a McGeady cross sent the ball looping over his own keeper, although Elia bravely headed off the line under intense pressure from Duff.
For their part, the visitors were a shadow of the team which had wrought such havoc in the past, although Given had to make a superb reaction save from striker Konstantinou after Duff had sliced Konstantinos Makridis' 15th-minute cross high into the Dublin sky.
Anastasiades' response was to shuffle his pack, with Andreas Papathanasiou coming on for late replacement Lambros Lambrou at the break and Georgios Panagi following him seven minutes later.
However, it was the home side who continued to hold the upper hand, although Richard Dunne had to make a solid block to prevent Given from having to deal with Christofi's well-struck 50th-minute volley.
The Manchester City defender came to the rescue again eight minutes later, denying Konstantinou after Makridis and Papathanasiou had opened up Ireland for the first time in the game.
Cyprus, with newcomers Papathanasiou and Panagi particularly prominent, were starting to find their range to stretch Ireland repeatedly.
But McGeady could, and perhaps should, have calmed the nerves with 15 minutes remaining when he was handed the chance to cap an enterprising night in style.
Glenn Whelan picked him out in space on the right and with Giorgallides advancing, he chipped the ball over him with the outside of his right-foot, only to see it sail agonisingly just over the crossbar.
The ever-industrious Kevin Doyle forced a one-handed save from Giorgallides with six minutes remaining, but it was Given who excelled himself once again at the death, blocking Christofi's goalbound drive with his legs.
Giorgallides kept out Duff in injury time after Keane had launched a counter-attack from his own half, but just as the tension became almost unbearable, the final whistle brought welcome relief.
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