Addicks punish Huth howlers
Charlton won 5-4 on penalties after Huth missed his spot-kick to add to his error in the first half of normal time.
The 21-year-old gifted Charlton an equaliser when his attempted back-header never reached Italian goalkeeper Carlo Cudicini and Darren Bent nipped in to score his ninth of the season.
The goal cancelled out skipper John Terry's 41st-minute header from Arjen Robben's corner and Huth compounded his first-half mistake by missing Chelsea's second penalty.
Mourinho made seven changes from the side which drew 1-1 with Everton on Sunday but it was still a team brimming with quality internationals.
The first quarter, predictably enough, was all Chelsea as Shaun Wright-Phillips and Michael Essien probed the Charlton defence in search of an opening.
In the 22nd minute a sweeping move down the left-flank almost brought the home side an opening goal.
Robben, having a quiet game by his own standards, cleverly fed the overlapping Bridge and the full-back delivered a perfect cross for Hernan Crespo to head narrowly wide of the upright with Andersen beaten.
Two minutes later Crespo was put clear down the left by Essien and Charlton's defence did well to clear the ball for a corner as Chelsea increased the pace.
Terry gave Chelsea the lead in the 41st minute when he headed Robben's corner firmly into the net from eight yards.
But Huth made a dreadful error on the stroke of half-time to gift Charlton an equaliser. The German tried to head the ball back to Cudicini but he did not apply enough power and Bent nipped in to fire past the stranded Italian.
In the 50th minute Terry was only a foot away from scoring his second of the night when his left-foot volley just veered away from Andersen's right-hand post.
Wright-Phillips and Gudjohnson then went close but the stalemate could not be broken by either side and the game went into extra-time and then penalties.
Charlton scored all five through Bent, Bothroyd, Matt Holland, Hermann Hreidarsson and Hughes but Huth's effort was saved by Andersen to send Charlton through to the fourth round.
: Cudicini, Paulo Ferreira, Terry, Huth, Bridge (Lampard 60), Wright-Phillips (Joe Cole 60), Essien, Geremi, Robben, Gudjohnsen, Crespo (Drogba 83).
: Andersen, Young, Hreidarsson, El Karkouri, Powell, Rommedahl (Thomas 64), Ambrose (Bothroyd 73), Murphy (Kishishev 82), Holland, Hughes, Bent.
: A Wiley (Staffordshire).