Liverpool, playing their first Premier League match without Luis Suarez, sold to Barcelona in the close-season, were far from their flowing best and laboured going forward without the Uruguay frontman.
But Sturridge – now Liverpool's main man in attack – saved the day with a predatory finish from four yards with just 11 minutes to play.
The hosts controlled the first half, but chances were few and far between against a Southampton outfit playing a league match under manager Ronald Koeman for the first time.
One of those opportunities did lead to the opener, though, as an exquisite Jordan Henderson throughball set up Raheem Sterling, who produced a cool finish midway through the first half.
Nathaniel Clyne's powerful effort levelled proceedings in the 56th minute and Liverpool, who finished second last term, were sloppy at the back after the break.
Brendan Rodgers' men could have trailed but Steven Davis missed a golden opportunity and was made to pay as Sturridge reacted quickest to Sterling's header to prod home.
There were still nervy moments for the home crowd, who saw Morgan Schneiderlin's fierce effort superbly tipped onto the bar by Simon Mignolet, before substitute Shane Long inexplicably headed the rebound wide, but Liverpool held on for victory.
Ex-Southampton man Dejan Lovren was one of two new Liverpool signings included from the beginning, alongside Javier Manquillo, while wantaway midfielder Schneiderlin started alongside four fresh faces for the visitors, who won the corresponding fixture last season.
Lovren's early touches attracted derision from the travelling supporters, but, while Liverpool controlled the opening stages, all they had to show for it was a pair of half-chances.
Sturridge first fired into the Kop before Sterling shot straight at Southampton goalkeeper Fraser Forster but a genuine piece of quality from Henderson helped them break the deadlock.
From inside his own half, the midfielder hit an inch-perfect pass with his left foot that split defenders Jose Fonte and Clyne to set Sterling free.
And the 19-year-old, who surged clear of the chasing Clyne, showed excellent composure to slot past Forster and open the scoring.
While a raft of senior players – and former manager Mauricio Pochettino – left Southampton in the close-season, the club have been able to hang onto James Ward-Prowse, at least for now, and the highly rated prospect almost levelled when a long-range free-kick caught the wind in the 34th minute and nearly crept in.
However, Liverpool goalkeeper Mignolet was alert to the danger and was also called into action on the stroke of half-time, doing well to tip a fizzing Schneiderlin effort over.
They were warning signs the home side did not heed, though, and Clyne drew Southampton level 11 minutes after the break.
After a thoroughly uninspiring start to the second half, Clyne played a neat one-two with Dusan Tadic, who sent the defender through on goal with a clever backheel.
And Clyne, who was allowed to run into the penalty area untracked by Lucas Leiva, hammered past Mignolet and into the top-right corner.
It could have got worse for Liverpool when Ward-Prowse centred for a free Davis in the penalty area with the hosts in disarray at the back, but the Northern Ireland international could only shoot at Mignolet after an excellent team move.
Rickie Lambert came off the bench to feature against his old club, but it was his strike partner, Sturridge, who stole in front of Clyne to score the winner, while Mignolet's heroics at the other end were just as crucial.
