A goal in each half from central defenders Robert Huth and John Terry kept Chelsea in the hunt to win four trophies in this season.

Huth, missing from the first team squad for two months after damaging his ankle on international duty, put Chelsea in command in the fifth minute when he rose unchallenged to plant Damien Duff's corner into the net.

The crossbar denied Huth a second goal before Terry finished off poor Birmingham with a powerful header from substitute's Frank Lampard's cross in the 79th minute.

Chelsea were quickly into their normal fluent mode against Birmingham and twice in the early minutes they caused City some jittery defensive moments.

Birmingham were expecting an onslaught as they opted to leave striker Emile Heskey on his own in attack and Jose Mourinho's Carling Cup finalists did not disappoint.

The Blues demonstrated a desire to cover themselves in more cup glory with a relentless drive on City's goal.

In the fourth minute Duff burst clear of the City defence and forced Maik Taylor into a diving save with a low drive.

But it was only a brief respite from the non-stop pressure and the opening goal duly arrived a mere sixty seconds later.

Defender Huth put Mourinho's men in control of the fourth round tie when he rose unmarked on the edge of the six-yard box to power a header beyond the helpless City 'keeper.

Birmingham were clearly rattled by the severity of Chelsea's opening salvo and it took them most of the opening quarter to readjust.

But with Heskey given a thankless task up against the formidable partnership of Terry and Huth at the heart of the home defence, City were predictably starved of openings.

It was the 19th minute before Steve Bruce's side found the confidence and the space to test Carlo Cudicini in the Chelsea goal.

City were further hampered by an enforced substitution in the 26th minute when the injured Martin Taylor was replaced by Olivier Tebily.

In the 32nd minute Duff should have made it two when Joe Cole put him clear of the City defence with a clever ball inside Tebily.

But the Republic of Ireland international, normally so deadly in such positions, squandered the opportunity by failing to hit the target.

Mourinho had made eight changes from the side which earned them a place in the Carling Cup final against Liverpool at Cardiff's Millennium Stadium next month but the disruption to normal service was minimal.

In the 41st minute it was left-back Wayne Bridge who turned master craftsman with a lovely through ball for Duff.

However, the Irishman's shot was deflected for another corner and when that arrived in the middle of the City penalty area moments later, Huth was denied a second goal by the width of the crossbar.

Chelsea swapped one rampaging winger for another during the interval with Mourinho deciding it was Arjen Robben's turn to terrorise the City defence instead of Duff.

But it was City who almost got on level terms in the 52nd minute when a cross from Julian Gray fell to former England midfielder Darren Anderton at the far post.

Anderton's volley was good enough to bring the best out of Cudicini and the Italian was forced to tip the ball over the crossbar.

Anderton was unlucky not to earn his side a penalty when his shot appeared to strike the upper arm of Terry inside the penalty area in the 56th minute.

Sixty seconds later City midfielder Robert Blake despatched a 20-yard shot that flashed narrowly wide of Cudicini's right-hand post as Bruce's side began to believe they could salvage something from this fourth round tie.

Chelsea should have put paid to any such thoughts in the 61st minute when Robben failed to make the most of a sweeping four-man move.

Glen Johnson sent Mateja Kezman free with a fabulous 40-yard pass and when the Serbian striker's cross was laid into Robben's path by Eidur Gudjohnsen, the Dutchman sent his shot a yard too high.

But it was Birmingham who were almost gifted an equaliser seconds later when Blake failed to capitalise on a dreadful back header from the normally reliable Terry.

In the 70th minute, only a brilliant reflex save by Taylor prevented Lampard from scoring Chelsea's second.

The midfielder's left-foot shot was destined for the bottom corner of the net until Taylor dived to tip the ball round the post.

Skipper Terry finished off Birmingham's FA Cup hopes in the 79th minute when he rose to head home Frank Lampard's cross.

Teams

Chelsea Cudicini, Johnson, Huth, Terry, Bridge, Cole, Smertin, Jarosik, Duff (Robben 45), Gudjohnsen (Drogba 65), Kezman (Lampard 60).

Subs Not Used: Pidgeley, Geremi.

Goals: Huth 6, Terry 80.

Birmingham Maik Taylor, Melchiot, Upson, Martin Taylor (Tebily 25), Clapham, Anderton (Yorke 76), Clemence, Carter, Gray, Blake, Heskey (Morrison 73).

Subs Not Used: Vaesen, Kuqi.

Booked: Upson.

Att: 40,379