Giroud opened the scoring early in the second half, and his replacement, Morata, added a late insurance goal. The Blues will meet Manchester United in the final on May 19.
Here are the key takeaways from the contest.
It wasn't a huge surprise to see cup goalkeeper Willy Caballero get the nod in goal for Chelsea, but Thibaut Courtois didn't take a spot on the bench, either, with Eduardo the back-up stopper.
The absence didn't appear to be down to health, according to Vaishali Bhardwaj of the Evening Standard:
One-Way Traffic at Wembley
Chelsea came out firing early and strung together several good chances in the first half, with Willian hitting the crossbar just seven minutes into the contest.
Eden Hazard and Giroud also had their looks, and Bleacher Report's Sam Tighe noted things were difficult for Saints:
The Blues' dominance resulted in the opening goal shortly after the restart, as Hazard beautifully set up Giroud, who used his quick feet to get past multiple defenders for the goal.
Giroud and the FA Cup
Speaking of Giroud, the Frenchman has built a fantastic record in the FA Cup over the years:
Long's Comical Miss
Southampton improved after Giroud's opener but failed to create a lot of chances. With few opportunities available, it was vital the team made the most of their chances, so when Shane Long rounded Caballero instead of pulling the trigger, fans were in disbelief.
Coral summed things up like this:
Cabellero's Heroics and Controversy
Former Manchester City stopper Caballero was anything but orthodox on Sunday, but the Argentinian made one key save, brilliantly keeping out a shot from Nathan Redmond.
He clashed with Charlie Austin on the resulting corner, getting the foul when many fans and pundits believed it should have been a goal:
Morata made a late cameo and doubled the lead just minutes after coming on, guiding home a header from a Cesar Azpilicueta cross.