A brace from the in-form Michael Fowler ensured his fourth goal in three games for Danny Cadamarteri's side. Burnley took the lead with just two minutes gone, before City equalised 20 minutes later. Fowler then snatched the Clarets' winner in added time to keep Burnley top of the table.
The home side got off to a dream start with less than two minutes on the clock played, Fowler burst forward on goal before coolly slotting past Tom Bilson in the City goal.
After the goal, the game very much settled down with neither side testing either goalkeeper.
However, the Sky Blues then had their equaliser with 25 minutes gone, Aaron Whitmore dinked the ball over Adam Bruce to draw things level.
Rhys Fenlon then came close to finding the goal, his effort from just outside the box was pushed wide by Bilson.
Shortly after, Chris Conn-Clarke was introduced and the Northern Ireland U17 international had a great chance, after his close range strike was denied excellently by Bilson.
City had a couple of opportunities to take the lead as the clock ticked on, Costelus Lautaru saw his header denied from a corner.
With minutes to go the Clarets had a great opportunity to take the lead, Fowler broke through on goal after latching onto Bruce's long ball, however his strike sailed well over the bar with an unmarked Mitch George lurking in the area.
However, the skipper did find the net with seconds to go deep into injury time, Conn-Clarke played a neat ball through to Fowler who fired it into the top corner past a stranded Bilson in the goal.
The Clarets remain top of the table after their third consecutive win and are next in action a week today at Watford on the 1st September.
Bruce, Patterson, Moss (Pruti 66), Taylor, Rain, Smith (Conn-Clarke 62), Kershaw (George 72), Yari, Mupariwa, Fenlon, Fowler.
Unused subs; Allen, Conley.