The Clarets raced into a 2-0 lead with two goals in as many minutes after the half-hour mark.
Mason Spence netted City's first after latching on to Charlie Henry's cross from the left before Billy Bricknell doubled the Clarets' lead. His initial shot ricocheted back into the path of him, allowing him to strike a thunderous volley into the corner.
The Shrimpers - who fielded an U21 squad - then halved the deficit when ex-Claret loanee Jason Williams profited from a goalmouth scramble.
Bricknell then restored City's two goal lead on the hour when his free-kick from distance flew underneath the wall before nestling into the bottom corner.
The Clarets then should've seen the game out but after Rory McAuley, City's influential centre-back and captain for the evening, was replaced, the defence fell to pieces and let the two goal cushion slip.
Southend's right-back met a lofted ball over the top, allowing him to lift the ball over the on-rushing Timms, before their number five headed a deep cross into the net after peeling off his man at the far post with twelve minutes remaining.
**Southend were unable to provide a teamsheet for us**