It was a fast start for the visitors as Ionut Nedelcearu hit the back of the net from a free kick inside the first two minutes of the game at Wrexham.
The hosts were stunned, but they were able to regain composure and keep decent possession of the ball.
Declan John came close to finding the equaliser after cutting inside following a charging run down the left, but his shot was saved.
Before the 15-minute mark, Burns managed to connect with John's cross into the box and sent his header into the back of the net to keep Wales in the game.
Burns tried to make things happen for Wales by breaking away from his marker and racing to the byline, but his cross was blocked and sent out for a corner, which came to nothing.