City midfielder Evans played the whole ninety minutes on Friday evening as Wales U21s secured a goalless draw away to Denmark in their latest UEFA U21s European Championship qualifier.
Centre half Burke also featured for the full game in England Under 20s' 2-1 win over Turkey on Saturday.
Burke and the rest of his England U20s team-mates will now face Germany on Tuesday in their final game of the Mercedez-Benz Elite Cup.
Fellow City defender Rory McArdle didn't feature this weekend, however, as Northern Ireland confirmed their place as winners of their EURO 2016 qualifying group with a 1-1 draw in Finland on Sunday.