Keatley kicked Ireland into a 12-3 lead to break Italy's resolve, then Conor Murray and Tommy O'Donnell scored tries after the hosts had hooker Leonardo Ghiraldini sent to the sin bin.
Italy finished with a flourish and Kelly Haimona thought he had scored a try, but it was ruled out because of the faintest of knock-ons by Sergio Parisse amid jeers from the Stadio Olimpico crowd.
Italy, who lost all their Six Nations matches last year, made too many elementary mistakes and never looked capable of repeating their 22-15 win of two years' ago.
Ireland suffered a blow before the start when Sean O'Brien, set to make his first international appearance for 15 months after undergoing two shoulder reconstructions, suffered a hamstring injury in the warm-up and was replaced by O'Donnell.
"It was a slog, any time you come to Rome you're expecting a slog but we knew if we kept chipping away, we'd break them down," Ireland's Rob Kearney told the BBC.
Keatley gave Ireland an early lead after George Biagi got into an offside position in what became a frustrating routine for the hosts.
Ireland were awarded another penalty when Luke McLean picked up the ball in an offside position and Keatley confidently sent his kick between the posts.
He increased the lead to nine points after Italy gave away another penalty for offside when second row Joshua Furno got on the wrong side of a maul.
Italy enjoyed a spell of pressure just before halftime and were rewarded when, following an Irish infringement at the maul, Haimona got them on the scoreboard with the last kick of the half.
Ireland began the second-half with more pressure and Keatley restored their nine-point advantage after Italy were penalised for wheeling the scrum.
However, Ireland rarely looked like scoring a try until Ghiraldini was sent to the sin bin.
Almost immediately, Ireland, who chalked up their eighth successive international win, won the ball at a line-out and Murray picked up the ball and dived over the line.
Two minutes later, O'Donnell slipped through a gap, shrugged off a tackle and ran from the 22-metre line to plant the ball under the posts. Keatley and Ian Madigan kicked the respective conversions.
(Writing by Brian Homewood; editing by Justin Palmer)
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