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The Spurs striker was joined on the score sheet by Kevin Doyle, the Reading forward netting the first for his country on his fifth appearance, with the easy win initiated by an own goal from Davide Simoncini.
While the scoreline failed to match the 13-0 and 7-0 hidings handed out to San Marino by Germany and the Czech Republic in their first two Group D matches, at least Ireland have a win under their belt.
San Marino were not expected to offer stern resistance, not when you consider they had lost all 36 of their previous European Championship qualifying games, conceding 163 goals into the bargain.
And Ireland weren't going to let their fans down on this night, the last time a soccer international would be held at Lansdowne and they only had to wait six minutes for the opening goal.
It was a moment Simoncini will want to forget in a hurry as it was his foul on Doyle that lead to Charlton's Andy Reid sizing up the free kick.
From 20 yards, Reid's left-foot curler struck Simoncini on the forehead, with the ball deflecting past wrong-footed goalkeeper Federico Valentini.
Doyle and Wigan midfielder Kevin Kilbane both had chances to add to the score at that stage, albeit with Ireland playing at a canter rather than the high tempo perhaps needed to make light work of their opponents.
After Keane had planted a 12-yard header narrowly wide from a Kilbane cross, Ireland added their second in the 24th minute, with the moment the 23-year-old Doyle had been waiting for.
Kilbane was again the supplier from the left, with Doyle's header crossing the line off the underside of the crossbar after looping over the outstretched grasp of Valentini.
Kilbane then proceeded to waste two headed opportunities, but at least he was in a creative mood as he instigated the 31st-minute move that culminated in Keane netting his first of the night.
Doyle and Reid played their part, with the latter playing Kilbane in on the overlap for a cross to an all-alone Keane who initially chested the ball down before side footing past Valentini.
Then 90 seconds before the break came San Marino's best chance of the match with captain Andy Selva curling a 25-yard free-kick wide of the left-hand post after he had been fouled by Paul McShane.
A slow start to the second-half was eventually punctuated in the 58th minute, with Keane sending Valentini the wrong way from the spot after McShane had been upended in the area by Simone Bacciocchi.
Again a further lull followed, with McShane going close with a header in the 70th minute before Keane completed his three-goal haul in the 85th minute.
Reid delivered a precise ball from the left into the heart of the area where Keane stooped low to head home from four yards.
In the closing stages centre-back Richard Dunne and Damien Duff came close to adding a sixth, but in the end a five-star show was enough for Staunton.