Jay Rodriguez gave Saints the lead midway through the first half but Chelsea took control to win the third round tie at a canter.
Demba Ba scored a brace on his Chelsea debut with Victor Moses, Branislav Ivanovic and a Frank Lampard penalty doing the rest of the damage.
But probably the biggest worry for Saints was seeing Fonte carried off with a knee injury.
Ba got life at Chelsea off to a fine start.
The 27-year-old completed his move from Newcastle to west London yesterday and took just 35 minutes to open his account for the Blues.
Rafael Benitez's side had fallen behind to a fine Jay Rodriguez goal but Ba quickly drew his new side level, getting the final touch on a goalbound Juan Mata effort.
Victor Moses' strike in first-half stoppage time gave Chelsea the lead, with Branislav Ivanovic heading the visitors further ahead seven minutes after the restart.
Ba put the tie out of any doubt in the 61st minute, linking up impressively with his new team-mates to slot home past Artur Boruc.
The Senegal international was denied a hat-trick goal by the Southampton goalkeeper, who was beaten from the penalty spot by Frank Lampard, equalling Kerry Dixon's all-time scoring record of 193 for Chelsea to put him joint second behind Bobby Tambling.
The match took a while to get going on a mild afternoon at St Mary's, with David Luiz's tame 13th-minute effort the first of note.
Play swung from end to end as both sides patiently waited for an opener, which went to the home side.
Jason Puncheon sent a fine through ball to Rodriguez, who took a touch before expertly slotting past Ross Turnbull with the outside of his right foot.
The 22nd-minute strike jolted the visitors into life and Eden Hazard soon came close with a curled effort that went narrowly wide of the far post.
Luiz had to react quickly to deny James Ward-Prowse at the other end after the teenager found space on the edge of the box, but the Blues were becoming an increasing attacking threat.
Ba's link-up play was improving as the half wore on and Saints were having to defend resolutely.
However, their resistance only lasted 35 minutes as the new boy opened his Chelsea account.
Hazard played through Mata, whose dink over Boruc was creeping in only for Ba to fire into the roof of the net.
Boruc was almost beaten again four minutes later, but fortunately his spill from a Moses strike went wide.
The Polish goalkeeper was looking rusty on what was only his second start since October 28 and soon fumbled a long-range Cesar Azpilicueta strike.
Chelsea were playing with new-found confidence and took the lead in first-half stoppage time, with Moses collecting a cutback from Ashley Cole to power home a low left-footed strike.
The Blues continued in the ascendancy after the restart, with Mata seeing a strike deflected wide by Guly do Prado shortly after the restart.
The Spaniard was involved yet again in the 52nd minute, sending over a left wing cross that Ivanovic headed home at the near post.
Only an excellent tackle from Luke Shaw prevented Hazard getting a fourth shortly afterwards, although Chelsea soon found the back of the next.
Having started the move, Ba showed excellent movement to latch onto a Hazard pass from the right to slot home under pressure from captain Jose Fonte.
The Portuguese defender looked to be badly injured in the challenge and was stretchered off, with Jos Hooiveld coming on in his place.
A great double save denied first substitute Steve de Ridder and then Steven Davis as Saints looked to claw a goal back, before Ba was denied a hat-trick by Boruc.
The Saints goalkeeper did excellently to stop the striker's header with his feet and had to be alert to deny substitute Lampard.
However, the midfielder did get on the scoresheet seven minutes from time.
Davis was harshly adjudged to have handled and the 34-year-old sent Boruc the wrong way to equal Tambling's record of 25 FA Cup goals for Chelsea.