Bradley Pritchard gave Charlton a fourth-minute lead before Johnnie Jackson doubled their advantage. Yann Kermorgant headed a third after 48 minutes before Stephen Dawson was shown a straight red for a lunging tackle on the Frenchman.
Callum Harriott made it four ahead of substitute Salim Kerkar making it five as Charlton claimed their ninth away victory of the season.
A horrible day for the home side was capped by a second sending off when Tom Kennedy brought down Ricardo Fuller when last man. And it was Fuller who made it six in stoppage time.
Just four minutes had been played when a Chris Solly cross found an unmarked Kermorgant whose shot could only be parried by Luke Steele into the path of Pritchard who tapped home.
Charlton doubled their lead after 19 minutes with a well-crafted goal.
The Addicks exchanged passes on the edge of the Barnsley box before Jackson feigned causing two home defenders to slide in.
The captain took the ball forward before firing a powerful effort between Steele's legs. Early in the second half a brilliant Wiggins cross evaded everyone but Kermorgant at the back post who headed home unchallenged.
It was 4-0 on 59 minutes and again it was down to a Steele error. Callum Harriott's 20-yard effort had power but it should have been a comfortable save for the goalkeeper. However he let the ball go in under his body and the match was well and truly Charlton's.
It got worse for Barnsley as they soon found themselves down to 10 men after Stephen Dawson went in strongly on Kermorgant and although he seemingly won the ball, referee Geoff Eltringham took little time to brandish a red card.
With 10 minutes left it was five when good hold-up play by Fuller brought in substitute Salim Kerkar who thundered an effort past Steele.
There was still time for another Barnsley sending off when a desperate Kennedy fouled Fuller when 25 yards out when the Jamaican had just the keeper to beat.
Fuller curled in a sixth in stoppage time after Barnsley once again failed to clear their lines.