Fiji were 17-7 ahead at the break, but Scotland's replacements, including two British & Irish Lions, helped turn the game in their favour and saw them join northern hemisphere rivals France and Ireland on two wins from their opening trio of games.
Scotland outscored Fiji by five tries to three, winning an important bonus point, with two for Jamie Dobie and one each for forwards Jonny Gray, Pierre Schoeman, and Scott Cummings. Fergus Burke converted three of the tries and George Horne one.
Captain Tevita Ikanivere, winger Selestino Ravutaumada and loose forward Elia Canakaivata were Fiji's try scorers with a single conversion from Isaiah Armstrong-Ravula.
The test exemplified the inconsistency which has frustrated Scottish fans, with the team beating Argentina away at the start of the month, coming close to upsetting world champions South Africa away in Pretoria last weekend, and, despite wholesale changes to the line-up, being expected to easily dispatch a Fijian side coming off a 73-8 hammering by England last week.
There was no reason to believe that would not be the case when veteran second rower Gray went over, after persistent pressure, for Scotland's first try in the 13th minute.
But there was an instant response from a line-out maul with Ikanivere dotting down on the line for Fiji's first try.
Three minutes later, Fiji showcased their thrilling ability to run the ball with a try that began in their own 25-metre area. The pace of right-wing Ravutaumada saw him go over after a clever kick forward.
They were further ahead six minutes from half-time, despite being down a man when Lekima Tagitagivalu was yellow-carded, when a kick fielded by Ravutaumada set up several attacking phases before Canakaivata burst through a leaky home defence to dive in under the posts.
Schoeman and Zander Fagerson were brought on to beef up Scotland's pack in the 48th minute and within five minutes Schoeman burst over to reduce the score.
Dobie, another replacement, then got the first of his pair of tries, picking up from a few yards out, to put Scotland back in front.
In the last six minutes, Cummings and Dobie scored two more tries to put some gloss on the score.
"We got loose and let Fiji into the game but we responded and the bench had a really big impact," said Scotland captain Stafford McDowall.
Fiji ceded home advantage for financial reasons and a crowd of 55,000 at Murrayfield will have helped their coffers as they hope to build a new stadium.
