The goal was in complete contrast to the game its self in which precious few opportunities were created as both sides struggled in difficult conditions.
The home side created the first opportunity of the evening with James O'Connor heading over a cross from Alan Mahon.
A mistake by right-back Graham Alexander allowed Jerome Thomas to race clear, but he blasted his shot wide of the target.
Clarets goalkeeper Gabor Kiraly was called into action to save at the second time of asking a long-range effort from Matt Holland.
Former Clarets striker Andy Gray had his first sight of goal three minutes into the second half, but shot over after collecting a knock down from Leroy Lita.
Another mistake from Alexander sent Gray clear into the penalty area, but Clarke Carlisle produced a goal-saving tackle at the expense of a corner, from which an unmarked Sam Sodje sent his header into the ground and over the cross bar.
Wae Elliott's quality strike after collecting a short pass from Robbie Blake sent the Turf Moor crowd ecstatic and the home side went close to extending their lead as left-back Jon Harley drove inches over the crossbar.
Charlton boss Alan Pardew made a double change midway through the half replacing Gray and Darren Ambrose with Chris Iwelumo and Luke Varney, but despite enjoying a reasonable share of possession, the visitors rarely threatened.
The nearest they came to earning a point followed yet another mistake by Alexander, but substitute Varney headed wide of the target.