The Scots' last championship triumph came in 1999, the last year of the old Five Nations before Italy joined the tournament.
They have not finished higher than third in the intervening 25 years but Gregor Townsend's team go into this weekend's clash in second place after showing that they are a match for anyone.
An agonising defeat to France in the second week despite being the better team for long stretches denied Scotland three wins from three.
As such, Scotland trail Ireland, who are at Twickenham on Saturday and are chasing the first double Grand Slam since France's in 1998, by six points.
Should England beat Ireland the title will go down to a final-day decider at the Aviva Stadium in Dublin later this month.
"We're into the last two rounds of the championship still in the mix, although it's an outside chance for the championship," said Townsend.
"There's a lot to play for this weekend and again in Dublin."
Italy are looking for their first home win in 11 years after only being denied a last-gasp victory last time out, over France in Lille, due to Paolo Garbisi kicking a penalty off the post.
The Azzurri's performances under new coach Gonzalo Quesada have merited more than the three points they have collected from their three matches.
But Italy have failed to make those displays count and are bottom of the table, trying to avoid their ninth straight wooden spoon.
"Scotland are a very good team. They should still be in the hunt for the Grand Slam as they should have beaten France," Quesada told reporters.
"They will obviously come here for a bonus-point win as they know that they can still win the title if they win their final two matches.
"It will be difficult but my team surprises me every day in training. They've worked very hard this week, they're motivated and know that if they play as well as they can they could make a whole country very proud."
Louis Lynagh, the son of Australia rugby great Michael Lynagh, will make his international rugby debut on Saturday after opting to play for the country of his birth.
Lynagh, 23, was born in Treviso where his father played and his mother is Italian, but he moved to England when he was four years old.
Last month Lynagh decided to return to Italy by switching from Harlequins for United Rugby Championship team Treviso.
He signed a two-year deal, with the option to extend the agreement until 2027, and will arrive ahead of the 2024/25 season.
Lynagh will play on the right wing as star man Ange Capuozzo starts at full-back and Monty Ioane on the left.
