Similarly to last season, striker Chris Wood gave the visitors the lead when converting Charlie Taylor's cross as the New Zealand international netted for the fourth league game on the bounce.
Burnley-born forward Harvey Barnes equalised after 20 minutes as the two sides went in level at the interval. The hosts then got their noses in front early in the second half when substitute Erik Pieters diverted Timothy Castagne's cross into his own net.
Full back Justin James stretched City's lead just after the hour when afforded a free shot on goal from close range courtesy of Ayoze Perez's centre while Jimmy Dunne, on his Premier League bow, headed past Kasper Schmeichel from Dwight McNeil's set-piece to give Burnley hope.
However, Dennis Praet eased the nerves and secured the points for the home side when thumping the ball past Nick Pope from the edge of the penalty area in the 79th minute.
Full back Justin James stretched City's lead just after the hour when afforded a free shot on goal from close range courtesy of Ayoze Perez's centre while Jimmy Dunne, on his Premier League bow, headed past Kasper Schmeichel from Dwight McNeil's set-piece to give Burnley hope.