Albion beat Charlton en route to the 2007/08 FA Cup semi-final the last time the two sides met at The Hawthorns.
Roman Bednar fired the Throstles into an early lead with James Morrison extending the Baggies’ advantage after the break.
However, after the hour mark Darren Ambrose clawed a goal back for Charlton with Chris Dickson scoring late on to level the tie.
Despite the late equaliser, the Baggies prevailed after penalties and went on to beat Peterborough United, Coventry City and Bristol Rovers to reach the last four, but were denied the chance to win the tournament by eventual winners Portsmouth.
