There has also been the biggest fall in youth unemployment since 2006, the Scottish Government said, with a drop of 28,000 in the number of 16 to 24-year-olds who are out of work over the last year.
Official statistics showed the overall jobless total – which includes those who are out of work and not eligible for benefits – fell over the the period October to December to 206,000.
That is a drop of 25,000 over the year, with the unemployment rate in Scotland now slightly lower than that of the UK as a whole.
The rate north of the border now stands at 7.7%, compared to 7.8% across the UK. The youth unemployment rate is also lower in Scotland, at 18.4%, than across the UK where it stands at 20.6%.
The figures for October to December showed that 74,000 young people were out of work north of the border.
Across Scotland the number of people out of work and claiming jobseeker's allowance fell by 600 from December to 137,000 in January – 5200 less than 12 months ago.
But the number of people in employment also fell by 11,000 over the period October to December to 2,461,000.
Across the whole of the UK, the jobless total fell by 14,000 between October and December to 2.5million.
The fall in unemployment was welcomed by both Scottish Secretary Michael Moore and Scottish Finance Secretary John Swinney.
Mr Moore said: "In difficult economic circumstances, I welcome the news unemployment fell by 13,000 during the last quarter of 2012."
Mr Swinney added: "Scotland has lower youth unemployment, higher youth employment and lower youth inactivity than the UK."