Musicians said Scotland's First Minister was in the supermarket with her husband when she spotted the troupe and stopped to praise their talents.
They said she jumped at the chance to conduct the six-piece and a video shows her waving her arms in the Asda supermarket in Fife.
Dressed in festive red, the SNP leader hopped up and down on the spot as the band played the festive tune.
She was picking up food for dinner with husband Peter Murrell when she stopped to watch Lochgelly Band perform.
She requested the brass band play Jingle Bells and one musician then shouted out: "Why don't you conduct it?"
Aisla McIntosh, band secretary and cornet player, said Sturgeon seemed "quite happy and upbeat" and posed for selfies before getting on with her shop.
Aisla, 26, said: "I was totally shocked to see her, as it's not every day that you get to meet the First Minister - let alone in an Asda!
"She was with her husband at the time, I think they were just stopping to pick something up for tea on their way home.
"To be honest, she just said 'hello' - and said how nice it was to see a brass band.
"We asked her if she had a song request, and when she came back with Jingle Bells someone in the band suggested - 'why don't you conduct it?'.
"She seemed on good form, in really good spirits."
The 165-year-old Lochgelly Band are one of the oldest brass bands in Scotland.
Ailsa McIntosh, Brian Sullivan, Stuart Sangster, Shona Moffat, Ron Rye and Neil McCormack performed from 11am until 3pm on Saturday (14) in Asda, Dunfermline.
Ms Sturgeon conducted for five minutes at around 2pm.
The Lochgelly Band will be out performing in various supermarkets before their annual Christmas Concert in Lochgelly on December 21.
A spokesperson for the group added: "The band were delighted to run into the First Minister on Saturday, and even more so that she took the time to stop and indulge us as a guest conductor, when she was just in Asda for her tea!
"We love to get out and about at Christmas, and this really has been the highlight of our carolling season so far.
"As a registered charity it's crucial for us to get out and about in the local community, especially as we're currently fundraising for essential renovations to ensure our band hall is compliant with health and safety standards."https://wonderful.org/fundraiser/christmas2019-236f13a1