The gap is measured by the average net circulation, figures for which were released on Friday. Average net circulation figures also include free give-aways.
The Sun's average daily sale in Scotland was 351,869 in January compared to the Daily Record's sale of 309,846.
However, the Sunday Mail, with an average sale of 378,321, remained Scotland's biggest-selling newspaper. Many other newspapers also enjoyed a rise in sales in January compared to December.