Sam Vokes opened the scoring in the 11th minute, heading home a Luke O'Neill cross before Lukas Jutkiewicz doubled the lead eight minutes from the break when he got on to a poor back pass and placed the ball past the City keeper.
Jutkiewicz it was who got the goal in the second half to complete the scoring, reacting quickly as a Vokes shot came off the post to tap in from close range.
The Burnley team was: Matt Gilks, Luke O'Neill, Michael Duff, Tom Anderson, Danny Lafferty, Ross Wallace, Cameron Howieson (Steven Hewitt 65), Steven Reid, Michael Kightly, Lukas Jutkiewicz, Sam Vokes.