"It was a slog," Ireland fullback Rob Kearney told the BBC.
"We knew that if we just kept chipping away and build some phases we would eventually break them down."
Keatley got Ireland off the mark on six minutes when stroking over a penalty after George Biagi was ruled offside and the No 10 extended his side's lead in the 21st minute from another kick when Luke McLean touched the ball in an offside position.
Ireland's lead was stretched to nine points five minutes before the break after Italy collapsed the maul but a subsequent Kelly Haimona penalty allowed the home side to go to half-time just six points behind.
Italy's line was almost breached by Robbie Henshaw in the early stages of the second half before Keatley made it 12-3 with another penalty.
However, Ireland finally got the try their pressure deserved when Murray crossed the line 15 minutes from time, immediately taking advantage of Ghiraldini's absence for being offside in the maul.
Keatley slotted over the conversion and O'Donnell ensured victory two minutes later after breaking Andrea Masi's tackle, with replacement Ian Madigan getting the conversion.
Haimona almost had a late consolation try for Italy but it was disallowed after the review showed Sergio Parisse had knocked on.
In Paris, France went ahead in a flowing encounter at the Stade de France through an early Lopez penalty before Laidlaw levelled matters with a penalty of his own after 13 minutes.
Two further Lopez penalties gave France a cushion but Fife rounded off some excellent Scotland pressure to leave just a point between the sides at the break.
Lopez extended France's lead to four points in a low-scoring second half but the home side failed to take advantage of their numerical superiority when Jonny Beattie was sin-binned for dragging down a French maul when a try looked inevitable.
Scotland threw everything at their opponents in a frantic finale but another Lopez penalty saw France to victory.
"We won so we need to accept this. Scotland played very well. We were not clinical or patient enough close to the line," said France coach Philippe Saint-Andre.
"It's a win but we should do a bit better than we did tonight."
France face Ireland in Dublin next weekend while England, 21-16 victors over Wales on Friday, entertain Italy and Scotland welcome Wales.
- AAP