Gordon Strachan's side secured the narrow victory thanks to Charlie Mulgrew's 39th minute goal.
Burke (pictured), who last appeared for Scotland back in 2006, played the first half at Aberdeen's Pittodrie Stadium.
Meanwhile, midfielder Callum Reilly won his first cap for the Republic of Ireland under-21s side.
The young Republic side recorded a convincing 3-0 win against a highly-rated Netherlands outfit in Dublin.
Midfielder Reilly played just over an hour before being replaced by Cian Bolger.
Elsewhere this week, Nathan Redmond completed 67 minutes for England under-19s on Tuesday evening as they swept aside their Danish counterparts 3-1 at Doncaster's Keepmoat Stadium.
The Blues winger played a key role in the win, as he set up the first two goals for the Young Lions.