CJ Stander scored a hat-trick for Ireland against Italy
Fresh from an opening day defeat at Murrayfield, Ireland flew out of the blocks and punched holes in Italy's defence almost at will.
Keith Earls was the chief beneficiary of the early pressure, twice crossing over untouched in the right corner inside the opening 26 minutes.
Flanker Stander also scored in the opening minutes after Simon Zebo's fine side-step and flat pass as the men in green jumped out to a 21-3 lead before half an hour had passed.
But Italy struck back almost immediately, winning a penalty at the scrum which allowed them to pin Ireland back in the corner.
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Two consecutive driving mauls were collapsed and the second resulted in a penalty try and a yellow card for lock Donnacha Ryan.
However, even with 14 men Ireland were rampant and Stander doubled his tally to secure the first ever four-try bonus in Six Nations history.
And South African-born Stander completed a magnificent hat-trick after the break when he picked a brilliant line from 25 metres out, bursting across from behind the breakdown to produce a finish fit for a winger.
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The performance was night-and-day when compared to Ireland's struggles in Edinburgh a week previous.
Ireland collected the bonus point in Italy
Italy were still able to wrestle some momentum as they obtained occasional dominance at the scrum but struggles at the line-out meant they were unable to turn possession and territory into points.
And with 12 minutes left replacement winger Gilroy profited from their wastefulness with a bending run to go under the posts for Ireland's sixth try.
Gary Ringrose added his second international try with a similarly impressive run-in from 50 metres out as Italy legs tired, running a quality line into wide-open spaces.
But Ireland weren't done yet, Gilroy connecting with a cross-field kick on the bounce and scoring Ireland's eighth try with three minutes left on the clock.
It is 17 years since Ireland had a hat-trick scorer, but they had two in Rome as Gilroy ran in a third out wide to complete a thrashing of the highest order.