The Blues will now take on United at Wembley in May, when Conte will renew his fierce rivalry with Jose Mourinho.
Conte's men started with blistering pace on the counter as Giroud dropped deep to feed Eden Hazard, who saw his rasping drive from the edge of the box fly just a few inches over Alex McCarthy's crossbar.
Hazard was at the heart of any Chelsea positivity. The Belgian scampered through the heart of midfield to find the feet of Willian, only for the Brazilian to see his shot cannon off the crossbar with McCarthy beaten.
Southampton offered very little going forward in the first period and gave both Charlie Austin and Shane Long very little to feed off. Mario Lemina arguably had Southampton's best chance when he drove a tame effort straight at Willy Caballero from the edge of the box.
The Blues might just have taken a lead into the interval, although Giroud could not make up his mind after being picked out by Fabregas, the Frenchman's eventual acrobatic volley flying over the bar.
Chelsea grabbed the crucial opener straight after half time thanks to Giroud, who showed outstanding composure to outmanoeuvre two defenders and prod home with the outside of his right boot to make it 1-0 in the 46th minute.
Southampton should have drawn level almost instantly when Austin pulled off an outlandish dummy to leave Long clean through on goal, although the striker's first touch was poor as he tried to round Caballero.
Saints grew in confidence and they twice came close to equalising. Substitute Nathan Redmond drove an effort under the body of Caballero, before the keeper seemingly fumbled over his own line only to be awarded a free kick when under pressure from Austin on the line.
Conte's men were shocked into action and Hazard almost made the final 15 minutes less tense with another testing drive from the edge of the area, which saw McCarthy tip the ball over the crossbar.
Hazard continued to be a nuisance all game and again he almost carved out a second, flashing across the box where Yoshida almost turned the ball into his own net at the back post.
Conte introduced Morata with under 10 minutes to play and the forward finally closed the game out having been on the pitch for just 86 seconds. Cesar Azpilicueta turned the ball towards the back post from deep on the right, leaving Morata to rise above his marker and head home.
Saints might just have made the closing stages a little more interesting, but Austin could only turn an effort back across the face of goal and off the far post as Chelsea were left to march into the final courtesy of a 2-0 win.
CHELSEA 3-4-3: Caballero; Azpilicueta, Cahill, Rudiger; Moses, Kante, Fabregas (Pedro 76'), Emerson; Willian (Bakayoko 64'), Giroud (Morata 80'), Hazard
SOUTHAMPTON (4-4-2): McCarthy; Cedric, Hoedt, Yoshida, Bednarek (Gabbiadini 78'); Bertrand, Romeu, Hojbjerg (Tadic 63'), Lemina; Austin, Long (Redmond 63')