|Olivier Giroud has scored 15 times in the FA Cup in his career|
Chelsea striker Giroud received the ball from Eden Hazard and jinked his way past two Southampton players in a crowded area before he stabbed the ball home.
Giroud was replaced by Alvaro Morata with 10 minutes to go and the substitute sealed safe passage with Chelsea's second when he headed in at the back post from Cesar Azpilicueta's cross.
Southampton went close with Nathan Redmond's low drive from distance while Charlie Austin hit the post.
It means Chelsea manager Antonio Conte will come up against managerial adversary Jose Mourinho at Wembley on 19 May.
There is no love lost between Conte and former Chelsea manager Mourinho, who have traded insults throughout the season.
The final is also repeat of 2007 when Mourinho guided Chelsea to a 1-0 victory over United in the first to be played at the rebuilt Wembley.