The Serbian striker headed home the first goal for Blues in the behind-closed-doors friendly at Wast Hills.
Blues’ American centre-half Will Packwood then doubled his side's advantage right on the stroke of half-time with a fabulous half-volley from the edge of the area, before the Clarets pegged a goal back after the break.
Blues regained their two-goal lead after a Burnley defender headed Ryan Higgins' dangerous cross past his own keeper and then the visitors' hit a late consolation goal.
Development squad boss Richard Beale was happy with his side's showing against a lively Burnley outfit.
"The most pleasing thing was the way we played in the first half," said Beale.
"We put together five or six really good passing moves where we could see that they have been listening to the things we’ve been doing in training in terms of breaking lines, playing forward and making runs off the ball.
"As a result Burnley had difficulty getting to grips with our system and we went 2-0 up.
"In the second half Burnley came out firing as you would expect and we conceded a poor first goal when one of our players was blocked off in the box and it allowed their player to have a free header.
"They were on front foot at that point but Ryan Higgins has then put a great ball into the box which has forced their defender to head the ball over his own goalkeeper to make it 3-1."
Beale added: "Burnley are a club that do things the right way. They beat Liverpool, with Suarez in the team last week, and they’ve got a good set of young lads who put us under a bit of pressure, so it was a good test for us."
Blues U21s: Townsend, Kelly, Packwood, Fry, Higgins, Moseley (Kalenda, 70), Adams (Truslove, 60), Asamoah (Cooper h/t), Gray, Zigic, Hales (Solomon, 55).