Managed by Mauricio Pochettino, the Saints took a commanding position early in the game, going two goals ahead in under 30 minutes - with Nathaniel Clyne and Rickie Lambert giving the home side the advantage.
Burnley, who were a Championship outfit at the time, pegged Southampton back early in the second half. Just before the hour mark, two goals in six minutes from Sam Vokes and Danny Ings leveled the score - setting up an interesting last half an hour.
Southampton's firepower off the bench was too much for the Clarets, though. Substitutes Jay Rodriguez and Adam Lallana both scored, ruling a late goal from Kevin Long as a mere consolation.
The F.A Cup tie between Southampton and Burnley was a showing of why they both had an eventual desire to sign the others main number nine.
Ings, who the Saints signed from Liverpool, equaled the scoring on the night to 2-2. The 27-year-old latched onto a long ball over the top from the Clarets defense, outpacing Jos Hooiveld before firing in from a tight angle.
The poachers' instinctive forward movement is a similar mold to that of this current campaign, with the lobbed pass remnant of how Jack Stephens has found his way to three assists this season.
As for Rodriguez, it was his goal that gave the Saints the lead once again on the night. After playing in James Ward-Prowse whos shot was originally saved, the current Burnley man smashed home the rebound.
Jack Cork also played in the red and white strip that match, providing the energy in the Southampton midfield. As well as this, Sam Vokes was also able to get on the scoresheet for the Clarets. The 30-year-old, who now plays in the Championship for Stoke City, is a Southampton fan.
Only James Ward-Prowse remains
After Maya Yoshida's departure in January, the only remaining players from the squad that still currently plays for Southampton is Ward-Prowse.
Club legend Kelvin Davis has retired, with Hooiveld and Rickie Lambert both making permanent moves to AIK and Liverpool respectively from the Saints before hanging up their boots.
Out of the remainders of the starting 11, Jack Cork moved to Swansea before transferring to Burnley, with Gaston Ramirez leaving on a permanent basis to Middlesbrough after two loan spells away from the club.
Unused substitutes Callum Chambers, Paulo Gazzaniga, Sam Gallagher, and Harrison Reed have all moved onto other English clubs (with the last of the four currently out on loan to Fulham).
Jose Fonte, who replaced Hooiveld with ten minutes remaining, left the club for West Ham, before moving to Chinse club Dalian Yifang. The Portuguese defender now plays for Lille in Ligue 1.
The highest-scoring contest between the two sides
The action-packed seven-goal game still stands as the highest-scoring tie between Southampton and Burnley, with the Clarets 4-2 victory in 1961 the closest to the accolade.
The way the match panned out, it had hints of the current Southampton side. Controlling the match, with a scoreline to empathise their quality, the home side let their lead slip, allowing Burnley back into the match, with a looming possibility the Championship side could progress. However, the red and whites were able to dig deep and regain their advantage - holding onto victory.
Sadly for the Saints, their hard-fought victory counted for very little, with their F.A Cup run ending in the fifth round.
The south-coast side felt confident of a cup run when they brushed aside Yeovil Town in the fourth round, but such optimism was put to an end at the hands of Sunderland, who knocked them out at the Stadium of Light.