After trailing 17-7 at half-time, Gregor Townsend's side turned the game around through a powerful second-half display, inspired by their bench. Replacements Pierre Schoeman, Scott Cummings and Jamie Dobie (2) all crossed as Scotland secured an impressive comeback.
Fiji, heavily beaten by England a week earlier, looked transformed, scoring three first-half tries through Tevita Ikanivere, Selestino Ravutaumada and Elia Canakaivata to dominate the opening 40 minutes.
Scotland struggled before the break but were revitalised by their substitutes, with regular skipper Sione Tuipulotu making a key impact as they overwhelmed a tiring Fiji to seal victory.
Stand-in Scotland captain Stafford McDowall praised his side's composure, insisting patience was crucial to eventually breaking down their opponents.
Scotland trailed at the interval after an impressive first-half display from Fiji, highlighted by a stunning solo try from Selestino Ravutaumada. However, the visitors turned the game around after the break, with the experienced replacements making a significant impact to seal a second win in three Nations Championship matches this month.
McDowall felt Scotland were rewarded for sticking to their game plan despite a frustrating opening 40 minutes.
"We spoke about how their result last week was a bit of an anomaly and we're going to see a different side this week.
"I thought they really brought it in terms of the fight and the way they played and the way they tried to clear it really good.
"I'm really proud of the boys. Some of the stuff in the first half wasn't perfect, but I think it was nine red zone entries so we're obviously doing something right but just couldn't quite get over the line.
"The way we stuck to it, we came out in the second half, stuck to what we talked about doing all week. And then the bench had a really good impact."
McDowall also revealed the message from head coach Gregor Townsend during the interval as Scotland looked to overturn their biggest ever half-time deficit against Fiji.
"Just stick to what we were doing. Like we said, we talked about during the week that they were going to have a moment. They were going to get a runaway try and they did.
"I was really happy with the reaction under the posts - everyone was really calm.
"We stuck to what we talked about during the week, just stick to our process. And we knew the work we were doing would eventually pay off."
Named player of the match, McDowall admitted he was not satisfied with his own contribution before half-time, feeling he struggled to impose himself. But he believed, like the team, he improved as the game progressed.
"I was probably a little bit disappointed at half time. I didn't think I'd maybe been involved as much as I wanted to be in getting my carrying game going.
"But I thought in the second half I managed to roll my sleeves up a bit and get involved a bit more, which I was happy with."