Sterling latched on to a defence-splitting pass from Jordan Henderson midway through the first half as he got his season off to a dream start with a composed finish beyond debutant goalkeeper Fraser Forster.
Ronald Koeman's men did threaten with James Ward-Prowse and Morgan Schneiderlin forcing saves out of Simon Mignolet, but it was Nathaniel Clyne who pulled them level with an emphatic finish just after half-time.
The Saints looked the most likely to take all three points for the majority of the second half but Sturridge ensured Liverpool got off to a winning start with a close-range finish on 79 minutes.
Brendan Rodgers handed Liverpool debuts to Dejan Lovren and Javi Manquillo, but fellow summer signings Rickie Lambert and Emre Can were forced to settle for places on the bench.
Forster, Ryan Bertrand, Dusan Tadic and Graziano Pelle made their competitive bows for the visitors, while Shane Long and Saphir Taider were named among their substitutes.
The hosts started brightly and began to dominate possession without really testing Forster. Sturridge and Sterling both looked lively in attack as Rodgers’ side patiently probed for an opening.
That eventually came through Sterling’s cool finish on the 23rd minute, but the 19-year-old owed a lot to his England team-mate Henderson for the through-ball which set him free on goal.
Henderson, who started alongside Steven Gerrard and Lucas Leiva in a three-man midfield, picked up the ball from deep and was able to cut through the Saints defence with an inch-perfect pass, finding the well-timed run of Sterling to slot beyond Forster.
Southampton responded in a fairly positive manner as debutant Pelle steered Schneiderlin’s low cross over the bar under heavy pressure from Lovren, before James Ward-Prowse almost caught Mignolet off guard.
Big things are expected of the 19-year-old midfielder this season and he was inches away from an equaliser as his wicked free-kick from the right sailed towards the far post, forcing a backpedalling Mignolet to tip behind for a corner.
Mignolet was then equal to Ward-Prowse’s curling effort from range with a comfortable save as the visitors looked to end the opening 45 minutes on a positive note.
Schneiderlin, who handed in a transfer request earlier this summer to try and force a move to Spurs, was hardly putting in the display of an unsettled player and he had Southampton's best chance of the half as Mignolet acrobatically tipped his strike over the bar.
Sterling then had chances either side of the break as he stung the palms of Forster before blazing a strike well over the bar from range.
Koeman's side started the second half brightly with Victor Wanyama dragging a shot wide and they soon found themselves level through the unlikely source of right-back Clyne.
Tadic had largely cut a frustrated figure for almost an hour into his Saints debut but he showed why a fee in excess of £8million was paid for his services as he backheeled into the path of Clyne, who sent Mignolet the wrong way.
The goal appeared to put Southampton into the ascedancy as they enjoyed the better of the play and an unmarked Steven Davis should have fired them ahead shorlty after the equaliser as Ward-Prowse teed him up for a strike which Mignolet was equal to.
Clyne made another marauding run into the area but was crowded out by a combination of Martin Skrtel and Glen Johnson, before Long, a £12million signing from Hull earlier in the week, was introduced for his debut on 73 minutes as Saints started to believe they could take all three points.
However, shortly after the arrival of Lambert for his Liverpool bow, it was the hosts who got the decisive goal as Sturridge got the deftest of touches on Sterling's return header to guide it beyond Forster.
Henderson's intial cross was headed clear and up into the air, but Sterling climbed highest to nod it back towards goal where Sturridge was lurking to get off the mark for the season.
There was still drama to come at the opposite end as Schneiderlin rattled the bar with a powerful strike and Long could only nod the rebound wide from six yards as Liverpool held off some late pressure to claim the win.