Kinghorn replaced injured Finn Russell in the starting XV on Saturday and took his chance with a match-winning 21-point performance, though in general there was a lack of creativity and invention from the Scots as winger Duhan van der Merwe also crossed for a score.
Italy defended heroically at times and scored their only try through fullback Tommaso Allan.
Trailing by five points, they camped on the Scotland try line for the final few minutes but the home side broke from their own 22 to complete the win
Scotland will enjoy a second top-three Six Nations finish in the last 10 years unless England get a big bonus-point win in Ireland later on Saturday.
Italy finished bottom of the table having lost all five fixtures, though their performances have been much improved this season.
"Italy have deserved more from this tournament and they put us under huge amounts of pressure," Scotland captain Jamie Ritchie said at the post-match presentation.
"Kinghorn did really well, he has been brilliant throughout the tournament when he has come off the bench and brought good tempo into our game.
"Before the Six Nations, I said I wanted five good performances. I think we gave four-and-a-half."
The error count from both sides will be uncomfortably high for the coaching teams but added to the drama in the closing 15 minutes as Italy stayed in the contest and came within inches of a famous win before the home side broke out and sealed the points.
Van der Merwe scored the opening try with a superb finish in the corner as he leapt for the line and managed to dot down while in the air, his body almost entirely in touch but no part on the turf.
The home side's ambition in turning down penalties paid off after numerous false starts when Kinghorn wrong-footed the Italian defence and crossed for an easy score, but Scotland's inaccuracy kept Italy in the game as the home side led 12-6 at the break.
Kinghorn added another score early in the second half when he burst through two tackles to dot down, but Italy hauled themselves back into contention when Allan crossed in the corner and landed a penalty.
Just as the visitors looked certain to score a second try and claim the win with seconds remaining, Scotland forced an error near their own line and broke the length of the pitch for Kinghorn to complete his outstanding day.
"We showed our rugby and our identity, and we are proud of that, but we need to improve to start winning at this level," Italy captain Michele Lamaro said.
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