The game was Scotland's first game in their opening round of UEFA European Under-17 Championship fixtures.
Sixteen-year-old Lang opened the scoring for his side with a 21st minute diving header. The win was then sealed by Dundee striker Craig Wighton's penalty conversion just into the second-half.
Scotland take on Belgium at Cappielow Park, Greenock on Wednesday, before returning to Kilmarnock on Saturday 29 March for their final group game against Romania.
It is understood that Lang will miss the Belgium game because of a suspension after an accumulation of yellow cards, but will be available for Saturday's match.