The win lifts the Saints up the third in the table – at least temporarily ahead of Leicester’s game with Brighton – as they celebrated the return of limited spectators to St. Marys with a dominant performance.
Southampton skipper James Ward-Prowse made his 243rd Premier League appearance for the Saints, moving up to joint-fourth with Francis Benali in the Saints’ leading Premier League appearance makers.
Saints made one change to the team that beat Brighton last Monday, with Danny Ings back into the starting line up in place of Moussa Djenepo. Chris Wilder made four changes to the Blades side that lost to Leicester last weekend. Enda Stevens and Ethan Ampadu returned to the starting eleven, whilst experienced pair Billy Sharp and Phil Jagielka also started on the south coast.
Southampton dominated the early stages, but were met with a stubborn Sheffield United defence as Adams had an effort blocked before Oriol Romeu fired wide inside the first ten minutes.
On 15 minutes Ings then had a chance to put the hosts ahead, but after a good ball through from Adams he was met with a fine save from Aaron Ramsdale.
Ward-Prowse then picked out Jannik Vestergaard, who after scoring against Brighton last weekend headed just wide of the top corner as the Saints continued to control proceedings.
However, despite their dominance the hosts were dealt a reminder just after the half hour mark when Stevens played the ball low into Sander Berge but he skewed his effort wide when well placed.
But it was the Saints who struck first after 34 minutes. Ward-Prowse’s free kick was headed away as far as Jan Bednarek, who helped the ball on to Adams and from close range he fired past Ramsdale.
Despite that, the Blades came out and started the second half the better, and John Egan came close to drawing the visitors level but could only head John Fleck’s corner wide.
Ings then fired over as the Saints looked to get back in control after good work from Theo Walcott and Kyle Walker-Peters down the right, before they doubled their lead in slightly fortuitous circumstances after 62 minutes.
Ings drove at the Blades defence before teeing up Armstrong, who shifted the ball onto his left foot before his low drive was deflected by Jagielka which took the ball past a wrongfooted Ramsdale.
After scoring some sublime free kicks in recent weeks, Ward-Prowse went close to adding another to that tally when his 25-yard effort skimmed the roof of the net before Vestergaard again met a corner from the Saints skipper, but headed wide.
It was then almost 3-0 with 15 minutes to go as Adams capitalised on Jagielka’s error and looked to tee up Ings, but Ramsdale was out well to save at the striker’s feet.
The hosts then did add a third seven minutes from time. Just two minutes after coming off the bench, Redmond played a neat give-and-go with Romeu and having held off George Baldock he slotted the ball into the bottom corner from twelve yards.