It was a somewhat harsh scoreline on Gary Johnson's side, whose attempts to win the fourth-round tie - and emulate the famous giant-killing side of 1949 - were valiant but ultimately fruitless.
An impressive 3,403 supporters made the trip from the West Country and saw their side produce a performance that belied their position 34 places lower in the football ladder.
There was a certain air of relief when Guly do Prado slotted home a penalty midway through the first half - the Brazilian's first goal in two years and 11 days.
Jay Rodriguez and Adam Lallana saw efforts hit the woodwork either side of the spot-kick, but Yeovil were proving a handful and it took 18-year-old Sam Gallagher to open his senior account with a fine solo effort to put the game to bed and bring a smile back to Southampton fans' faces after a difficult few weeks.
The Glovers began brightly at St Mary's, with Ishmael Miller causing a nuisance from the outset on his first appearance since he rejoined Gary Johnson's side on loan from Nottingham Forest for the rest of the season.
The 26-year-old was full of running and forced a corner off Nathaniel Clyne in the 12th minute, with Shane Duffy's header from the resulting corner on target but without the power required to threaten Kelvin Davis.
Yeovil continued to push with the backing of the vociferous travelling contingent and the hosts were fortunate that James Hayter was unable to get a telling touch on a clever ball behind their defence.
It appeared to be the shot in the arm the hosts needed, leading to a flurry of shots in quick succession.
Lallana, whose professional debut came in a League Cup match against Yeovil in 2006, saw a shot blocked before Rodriguez was thwarted by Marek Stech, before the latter saw a powerful header rattle the crossbar.
Saints continued in the ascendancy and the opening goal arrived after 23 minutes, with referee Phil Dowd pointing to the spot after Duffy was adjudged to have handled in the box.
Rodriguez looked set to take the resulting penalty but handed the ball over to Do Prado, who sent Stech the wrong way for his first goal since January 14, 2012.
Lallana flashed a strike wide and then saw a cross-cum-shot skim the bar after Yeovil had a penalty shout of their own waved away, before Davis' reactions kept Saints ahead.
Good play down the left between Joel Grant and Joe Ralls saw the ball played in for Hayter, whose goalbound effort was denied by a point-blank, if unorthodox-looking, stop by the Saints goalkeeper.
The Somerset club did not take long to threaten again when play resumed for the second half, with Luke Ayling seeing a 20-yard effort impressively pushed around the post by Davis.
Yeovil continued to push forward in numbers with John Lundstram having an effort on goal, but such attacking impetus was seeing Saints have opportunities at the other end.
Rodriguez saw a shot deflect behind and James Ward-Prowse saw an audacious dipping effort go close, with Clyne and substitute Gallagher soon forcing Stech into saves of differing quality.
Lundstram saw a venomous strike blocked by Shaw as Yeovil attempted to grab a leveller, although Saints went clear with 20 minutes remaining.
Gallagher, on for Do Prado in the 56th minute, showed impressive poise and skill to jink clear and fire past Stech from an acute angle.
It was a fine first goal by the teenager and one he hoped to add to soon after, although his attempt from a tight angle was cleared away.
Substitute Steven Davis saw an attempt impressively clawed away by Stech late on, with the Czech also denying Gallagher after the forward made himself space with impressive control.