The Irish will need to repeat that against France next Saturday in Paris to assure themselves of the title.
"There was a lot of good play today," said captain Johnny Sexton. "However, France are an outstanding team and we have our work cut out.
The Italians had caught the Irish on the hop early on.
It was, though, a false dawn for the visitors.
Frequent indiscipline by the Italians prevented them making inroads into the Irish 22.
As Keenan trotted back to the halfway line, Sexton converted brilliantly from the touchline for 17-3.
Sexton converted for a 24-3 half-time lead and leaving them one try shy of the bonus point win.
Right on the buzzer, replacement hooker Dave Heffernan added another try, three years after he made his previous Test appearance.