The strike which sealed the contest came in the 72nd minute, but was not without controversy, being scored after the Southampton defender Jason Dodd had not been allowed back on to the pitch after receiving treatment.
A throw-in by Steve Staunton was headed on by Paul Ince and Owen, unmarked in the box - partly due to Dodd's absence - made no mistake in putting it in the net.
The Southampton manager, Dave Jones, said afterwards: "I don't understand the ruling. You can't blame the referee for implementing it, but I don't understand why the lad couldn't come back on the pitch when he was fit to."
It was a justifiable point, but the end result was a fair enough representation of the match. Liverpool had attacked from the start, with Ince attempting a 20-yard shot in the first 30 seconds, an effort that was pushed past the post by Paul Jones in the Southampton goal.
Three minutes later, after a typical run from Steve McManaman - ostensibly performing a playmaker's role in the centre, but favouring the left side for most of his forays - the ball fell to Owen. His shot was not powerful, but it still required the deft reflexes of Jones to put it wide.
Southampton were forced to substitute John Beresford a few minutes later following a challenge by Veggard Heggem, but the home side recovered from the early Liverpool pressure to take the lead in the 36th minute.
Carlton Palmer fed the ball to Ripley on the right, whose cross was met in the box by Egil Ostenstad, who headed home. The advantage was short- lived, however, as within two minutes Owen had fed a similar cross on to the head of Karlheinz Reidle at the other end and the German equalised.
In this fixture last season, which finished 1-1, Reidle also scored for Liverpool - and coincidentally also with a headed goal from a cross in the same minute of the first half - and Southampton then equalised with a goal from Kevin Davies - now gone to Blackburn - to take a share of the points. Late in the first half yesterday, Southampton nearly took the lead when what looked like a speculative cross from Dodd had to be tipped over the bar.
The resulting corner fell to Ripley outside the box, but his powerful effort flew over the bar. Owen threatened early in the second half when a deft turn and pass from Riedle left the young striker with the ball at his feet and heading for goal. His fluidity gave him the chance to put Liverpool ahead, but Jones managed to foil his shot, holding the ball after a full-stretch dive.
Southampton countered, again through the work of Ripley, who was set free down the right wing and should have carried on to take a chance. Whether through misplaced selflessness - or more likely the pathological fear of shooting which often dogged him at Blackburn - he did not try a shot.
Instead, by the time Ostenstad was ready to receive the cross, he was surrounded by Liverpool defenders and the move was wasted. Owen's goal followed not long after and there was little Southampton could do to steal a draw, even with the late introduction of Matt Le Tissier, who may find himself a bench player more often than not this season.
The Liverpool co-manager, Roy Evans, who said after the match that long- term injury victim Robbie Fowler was close to resuming light training again, was full of praise for Owen.
"He's always going to get chances to score but it's about the team, he'll tell you that himself," he said. "He's an exceptional young lad and the first goal was down to him and other players getting the ball forward."
Goals: Ostenstad 1-0 (36); Riedle 1-1 (38); Owen 1-2 (72).
Southampton (4-4-2): Jones; Dodd, Hiley, Lundekvam, Beresford (Bridge, 7); Ripley (Beattie, 76), Palmer, Dryden, Oakley; Ostenstad (Le Tissier, 67), Hughes. Substitutes not used: Howells, Moss (gk).
Liverpool (4-3-1-2): Friedel; Heggem, Carragher, Babb, Staunton; McAteer, Ince, McManaman; Berger (Harkness, 67); Riedle, Owen. Substitutes not used: Leonhardsen, Thompson, Kvarme, James (gk).
Bookings: Liverpool Riedle, Heggem, Harkness.
Referee: P Alcock (Kent).
Man of the match: Owen.