Smarting from defeats at the hands of Wales and France, Gregor Townsend's side ran in five tries to win the Cuttitta Trophy in Rome on Sunday (AEDT) and move above Wales into fourth place.
Sam Johnson scored the opening try before Harris crossed twice, with Darcy Graham and Stuart Hogg getting in on the act after the break.
Callum Braley went in for a first international try in the first half and Ange Capuozzo scored a debut double, but the Azzurri's losing Six Nations run was extended to 36 matches on the penultimate weekend of the tournament.
Paolo Garbisi's penalty gave Italy an early lead, but Scotland was in front when Johnson finished in the right corner after George Turner had powered down the other flank to put Italy on the back foot.
Ali Price was the architect for a second try on the break after 21 minutes, intercepting Braley's pass deep inside his own half and bursting forward before whipping a pass out to Kyle Steyn, whose clever kick over the top enabled Harris to touch down.
Finn Russell added the extras, but Italy cut the gap to only two points after Pierre Bruno's brilliant offload on the touchline in the right corner put a try on a plate for Braley and Garbisi sent an excellent conversion between the posts.
Italy's joy was short lived, though, as Harris surged over for his second score late in the first half to round off a well-executed Scotland move.
Graham showed pace and power when racing through the middle to reward more Scotland pressure with another try early in the second half and Hogg darted over in the left corner after taking a fine pass from the impressive Price.
Russell expertly converted from wide on the left for a fourth time and the points continued to come, with Capuozzo wriggling his way over twice in a promising cameo off the bench, but Scotland was a comfortable winner.