The hosts' Danish defender heads in just before the break in a game dominated by Brendan Rodgers' side as Saints remain in the Premier League relegation zone.
A dominant performance from Liverpool saw plenty of action in the Southampton area, but a lack of clinical finishing in front of goal. Daniel Agger, however, was able to finally break the deadlock a few minutes before half-time with a strong header into the top corner of the visitors’ goal.
The hosts continued their confident performance into the second half, but once again failed to convert chances into goals and towards the end of the game looked to protect their tender lead.
There was encouraging news for the Liverpool camp in terms of team news, as midfielder Lucas was deemed fit enough to make his first start for the Reds since their 2-2 draw with Manchester City in August. Stewart Downing and Jordan Henderson were dropped in favour of the Brazilian and Jonjo Shelvey.
Meanwhile, Southampton manager Nigel Adkins made no changes to his starting 11 for the fourth game in a row.
The hosts were perhaps the brighter of the two teams in the first 10 minutes, with Glen Johnson almost putting Liverpool one to the good with the deftest of touches from a Luis Suarez ball into the front post.
Jonjo Shelvey was next up looking to put the home side ahead, the midfielder unsupported and surrounded by defender, the young attacker took on the shot and forced a parried save from Paulo Gazzaniga.
A similar situation some minutes later saw Suarez in the same scenario, but this time with a little more space to have a go on goal, with Southampton’s Argentine ‘keeper saving the Uruguayan’s shot a little more confidently this time around.
Continued pressure from Brendan Rodgers’ team had the Southampton defence struggling for composure and the likes of Suarez and Shelvey were fast becoming a real bugbear for visitors. However, the lack of a clear sight on goal for Liverpool meant that true chances were not as frequent as they perhaps should have been.
Liverpool deservedly took the lead after what had been a predominately imperious first-half for the hosts. A cross from Johnson found Agger on the penalty spot and the Dane directed the ball into the top corner with a great header past Gazzaniga.
After the break, Liverpool continued their dominance and pushed immediately for a second.
Suarez looked to lead the attacking line for the Reds, but chance after chance was either thwarted by the Southampton defence or squandered as a result of the hosts’ own lack of clinical ability in front of goal.
It looked as though Jose Enrique might be the man to double Liverpool’s lead, but the full-back’s effort at an angle was poked out for a corner by his marker. Gerrard followed up the attempt at the resulting corner, but the Red’s captain could get his shot on target.
Liverpool’s display looked to come off the boil in the later stages of the game and through their failure to double their lead, looked instead to protect the slender one they currently had. However, this lead to a shakey end for the hosts and could have lost two points thorugh a lack of composure.