The first half was a tight and at times scrappy affair, with neither side really in control of the ball for long periods, and chances on goal hard to come by.
Southampton made the better start with trying to use Adam Lallana to good effect in particular, but Simon Mignolet was largely untroubled after Lallana sent an early volley well over the bar.
At the other end, Liverpool got into their stride and tested Artur Boruc a few times, but the Polish keeper was equal to the task of keeping a Steven Gerrard free-kick and a Victor Moses shot at bay.
The most talked-about moment of the half was certainly a potential penalty call Daniel Sturridge thought he should have had after Dejan Lovren tripped him in the box. The referee, however, chose not to award a spot-kick, and the half finished goalless.
It was looking like the kind of game in which a mistake might make the difference, and so it proved, as sloppy play between Kolo Toure and Martin Skrtel led to a corner for Saints, which Lovren headed into the net for the opening goal.
Osvaldo almost made it two straight after, but for a good Mignolet save, while another Gerrard free-kick tested Boruc. Mignolet then had to be at his best to make a triple save to deny Luke Shaw, as Southampton continued to have the greater threat.
The expected late onslaught from the home side never arrived late on, as they surrendered their unbeaten record with rather a whimper.
Often overooked what a mess Liverpool's central midfield area has been under Rodgers, his supposed area of expertise. There's nothing there.— James McManus (@JamesMcManus1) September 21, 2013
Key Player Grades
Daniel Sturridge: D
A quiet first half for the Reds' top scorer, who was offered very little service in the absence of Philippe Coutinho and resorted to a couple of speculative long-range efforts. After the break, though, Sturridge faded from the game altogether, not making his usual runs behind the defence and curling a few overly ambitious efforts from range when a pass might have been the better option. A first poor performance of the season.
With Southampton having few chances in the first half, Lambert was restricted to dropping deep to try and aid the buildup play, which he did relatively well as always. One half-chance fell his way in the box, but he scuffed his effort. He was replaced midway into the second half, limiting his involvement.
Victor Moses: C+
In the absence of Coutinho, Victor Moses was one of the home side's only real threats in the final third. A series of surging runs in the first half, and one fierce shot, were as close to a goal as Liverpool managed to come. He was marginalised after the break as the Reds failed to attack cohesively.
After their first defeat of the campaign, Liverpool now face Manchester United in a League Cup third-round clash, where Luis Suarez will mark his return from suspension. Southampton have two winnable home games coming up, in the cup against Bristol City and then the league against Crystal Palace.