Flyhalf Finn Russell, replacement centre Matt Scott and wingers Tim Visser and Tommy Seymour scored tries as the Scots earned a bonus-point win and protected their fifth place in the world rankings ahead of the 2019 World Cup draw.
Italy, who lost all five matches in the tournament, failed to register a point as flyhalf Carlo Cana missed three penalties and the backs fluffed two clear try-scoring chances early in the second half.
The Scots, humbled 61-21 by England last weekend, climbed to second in the standings before the day's later matches after notching a fourth consecutive home win for the first time since 2006.
"I would like to thank the players and everyone for the last three years it has been fun," New Zealander Cotter told the crowd in an emotional farewell.
Fullback Stuart Hogg got Scotland off the mark with a penalty after five minutes before Cana missed a chance to level when he pulled his kick wide from a good position.
That miss summed up Italy’s miserable afternoon even if it took the home side nearly half an hour for their first big breakthrough.
Following a penalty lineout, scrumhalf Ali Price passed to Russell on the blind side and the flyhalf darted between two defenders to score the first try.
Scotland changed ends 15-0 up after Scott, who had come on for the injured Huw Jones, touched down after Hogg had tapped back Price’s chip into the corner.
Read the full article on eurosport.co.uk: Scotland thump Italy to finish Six Nations in style