Tonda Eckert made two changes to the starting lineup for the trip to Hillsborough, opting to give Cameron Bragg a runout in place of Flynn Downes and bringing back Shea Charles for Casper Jander in a completely overhauled midfield.
After an impressive 70 minutes on Tuesday night, Cyle Larin kept his place up front with Ross Stewart remaining on the bench.
Southampton started brightly and were almost a goal up after 8 minutes when Finn Azaz presented Cyle Larin with a good chance from a tight angle inside the six-yard box but his effort was smothered by Seny Dieng.
James Bree, who scored on Tuesday, made a period of pressure count when he prodded home a Léo Scienza cross in the 17th minute, which had been flicked on by Cyle Larin.
Sheffield Wednesday 0 - 1 Southampton
Southampton dominated for the next fifteen minutes but failed to create any meaningful chances. Finn Azaz wasted an opportunity to present Kuryu Matsuki with an easy chance by over-hitting a lofted pass across the penalty area and beyond the Japanese midfielder's extended right foot.
A delicately weighted pass put Cyle Larin through on goal in the 40th minute, but his shot was scuffed wide of the far post as Dieng narrowed the angle.
A foul on Matsuki on the edge of the box earned Southampton a free-kick in a dangerous area on the stroke of half-time. Ryan Manning got the ball up and down quickly over the Wednesday wall and into the near corner beyond Dieng's outstretched left hand. Manning's brilliantly executed free-kick was his sixth goal of the season.
Sheffield Wednesday 0 - 2 Southampton
The Saints went into the break two goals to the good, deservedly so. Southampton had restricted Wednesday to a couple of long-range shots and completely dominated possession and territory.
Had Larin done better with either of his two close-range efforts, the Saints could have been out of sight by half-time.
Half-Time: Sheffield Wednesday 0 - 2 Southampton
Scienza should have put his side 3-0 up, five minutes into the second half, after dribbling his way inside. His shot was tame and easily saved by Dieng.
Southampton took their foot off the gas a few minutes later, and Wednesday clawed their way back into the game when the Saints failed to clear a corner. Jerry Yates took advantage as the ball came back into the box, slotting home from close range.
Sheffield Wednesday 1 - 2 Southampton
Jamal Lowe forced Daniel Peretz into action on the hour when his low shot from the edge of the area failed to trouble the Saints keeper.
Another Manning free kick was destined for the back of the net before it was deflected wide for a corner in the 70th minute. From the resulting corner, Taylor Harwood-Bellis hooked in Léo Scienza's inswinging cross to make it 3-1.
Sheffield Wednesday 1 - 3 Southampton
Quick interplay between Scienza and Manning put the Brazilian back in again in the 75th minute. His shot was weak again and failed to beat the Wednesday keeper.
Southampton brought on Cameron Archer, Tom Fellows, Nathan Wood and Samuel Edozie for Larin, Matsuki, Bree and Scienza, respectively.
With just a few minutes left of the match, Manning slid Edozie in down the left and into the box. Edozie failed to hit the target with a lame shot, which drifted weakly into the side netting.
As the match entered additional time, Wednesday should really have got a second goal. A shot deflected off Gabriel Otegbayo, and Peretz did brilliantly to keep the ball out. However, the ball fell to Yates, who slipped at the vital moment.
Full Time: Sheffield Wednesday 1 - 3 Southampton
Southampton have now gone eight matches unbeaten and remain seventh in the table, four points behind Wrexham in sixth.