The fixture was a meeting between the two sides yet to win a game in the tournament this year and nerves were clear in a scrappy affair with a high error count.
A great solo try from Stuart Hogg was the highlight of the first half as the Scotland captain ran from inside his own half before finishing in the corner.
Scotland pulled clear in the second half when Chris Harris powered through the Italian defence to touch down, before Adam Hastings ran in under the posts to put the result beyond doubt with one minute remaining.
Scotland, who earned losing bonus points in their opening two matches, move ahead of Wales and England into third place on six points, while Italy remain bottom without a point.
Wales play France later today and England take on Ireland tomorrow.