BBC SPORT | Football | League Cup | Man Utd 1-2 Chelsea

Duff's 50-yard set-piece was intended as a cross but found its way into Tim Howard's net to decide a tight contest.

Frank Lampard had given Chelsea the lead with a powerful angled shot before United's Quinton Fortune had a penalty appeal turned down.

Ryan Giggs superbly chipped in to give United hope but Duff had the last word.

The much-anticipated match, delicately poised at 0-0 following the first leg, had been given more importance when both managers sent out full strength sides.

United skipper Roy Keane was making his first start of this season's competition while Chelsea boss Jose Mourinho, who was celebrating his 42nd birthday, dropped regular Carling Cup and second choice keeper Carlo Cudicini for Petr Cech.

It was the visitors who conjured up an early chance when Duff produced some trickery down Chelsea's right flank and whipped in a low cross from which Lampard flashed a shot wide.

But United looked the more at ease as they confidently passed the ball around trying to prise an opening through the tightest defence in the country.

A Louis Saha run caused some panic in the Blues backline only for the striker to fall over before he could get a shot in.

United right-back Gary Neville stole into the visitors box to meet a Giggs corner and knew he had wasted a good chance after seeing his shot curl away from goal.

His frustration was compounded when Chelsea took the lead with a classic sucker punch.

Lampard started the move with a pass to Arjen Robben and he found Didier Drogba who, in turn, cut inside Neville and slid a ball to Lampard.

The England midfielder finished off his 50-yard run into the box with aplomb by taking a touch before angling in a shot.

United, despite their superior possession, had failed to work a single shot on Cech's goal.

But they were left feeling aggrieved after referee Rob Styles looked to harshly deny them a penalty when Wayne Bridge clipped the legs of Fortune.

United were limited to shots from distance after the interval and only two smart saves from Howard kept the Old Trafford side in the game.

The American kept out another Lampard strike before denying Robben following a slick Chelsea move.

A battling United were then rewarded for their persistence when Giggs chipped over Cech from Neville's defence-splitting ball.

But Howard was undone by the curl on Duff's free-kick as it bounced agonisingly into his net to give the Londoners the lead after 85 minutes.

The home side piled on the pressure and Mikael Silvestre had a header cleared off the line by Wayne Bridge while Cristiano Ronaldo forced Cech into a vital save.

But they could not stop Ferguson's record of not having lost a domestic semi-final with the club being broken as Chelsea set up a final with Liverpool on 27 February.

Booked: Keane.

Goals: Giggs 67.

Chelsea: Cech, Paulo Ferreira, Gallas, Terry, Bridge, Makelele, Lampard, Tiago, Robben (Cole 90), Drogba (Gudjohnsen 68), Duff (Jarosik 87). Subs Not Used: Cudicini, Huth. Booked: Makelele.

Goals: Lampard 29, Duff 85.

Agg (1-2)

Att: 67,000

Ref: R Styles (Hampshire).