Liverpool went ahead with a confident finish from Sterling in the 23rd minute, but were pegged back 11 minutes into the second half when Nathaniel Clyne blasted home.
The home side, who were far from their fluent best in their first competitive game following the sale of Luis Suarez to Barcelona, were given a few late scares as Southampton grew in confidence.
But Sturridge ensured last season's runners-up made a winning start to the new campaign when he got on the end of Sterling's header in the 79th minute to nudge the ball home.
Liverpool handed competitive debuts to Croatia centre-back Dejan Lovren, who they signed from Southampton, and Spanish right-back Javier Manquillo.
The visitors, who sold five key players during the off season, included new signings goalkeeper Fraser Forster, winger Dusan Tadic and striker Graziano Pelle, while on-loan Chelsea defender Ryan Bertrand started at left-back.
Brendan Rodgers's side began confidently and striker Sturridge flashed a long-range effort over the crossbar, although Forster did not look worried by it.
The home crowd called for a penalty in the 12th minute when Maya Yoshida got himself tangled up with Sturridge, but the offence occurred just outside the area and referee Mark Clattenburg waved away their appeals.
Liverpool's dominance eventually told with a goal midway through the first half.
Jordan Henderson, who harried the Southampton players throughout, stole the ball in his own half and showed brilliant vision to send Sterling clear with an exquisite left-foot pass.
- Tadic's brilliant skill -
The 19-year-old England winger escaped the attentions of both Jose Fonte and Clyne and calmly stroked the ball past Forster as he tried to narrow the angle.
Shortly afterwards, a dangerous curling free-kick from James Ward-Prowse towards the back post caused Liverpool goalkeeper Simon Mignolet to make an awkward save.
Ronald Koeman's Southampton grew in confidence and Morgan Schneiderlin forced Mignolet to save in more orthodox, and spectacular, fashion just before the interval with a bending effort from 25 yards.
Forster was called into action again in added time in the first half when he parried Sterling's shot from just outside the penalty area.
Southampton's bright finish to the half continued after the break and they equalised in the 56th minute with a well-worked goal that owed much to a brilliant piece of skill from Tadic.
Clyne played the ball into the feet of the Serbia international and he expertly flicked the ball back into the path of the right-back, who fired high into the net from the corner of the six-yard box.
Southampton should have taken the lead when another intelligent ball from Tadic found Ward-Prowse, who teed up the unmarked Steven Davis 10 yards from goal, but he tamely side-footed the ball, allowing Mignolet to save.
Rodgers introduced former Saints striker Rickie Lambert for the tiring Philippe Coutinho in the 76th minute, in a bid to add more physical presence in the final third, and Liverpool's winner moments later certainly had more of a direct approach to it.
Southampton failed to clear a cross from the right flank and Sterling headed the ball forward into the path of Sturridge, who scruffily flicked the ball past Forster and into the net from close range.
Southampton squandered a late chance to equalise when Mignolet pushed a well-struck Schneiderlin shot onto the crossbar and substitute Shane Long headed the rebound past with the goal at his mercy.