The Reds had taken just one point from their previous two games, played away from home last week, so they would have been pleased to take all three this time around as they seek to get closer to the top six of the table again.
For Southampton, the result brought to an end their four-game streak of two wins and two defeats, and they remain in the relegation zone in the league.
Liverpool dominated the first half, but it took until the 42nd minute for them to take the lead thanks to Daniel Agger's header into the top corner. Last season's toughest opponent, the woodwork, also made a return to Anfield as both Jonjo Shelvey and Luis Suarez struck the post and crossbar.
The second half yielded no further goals—here are six things we learned in the game.
The first big positive for Liverpool from their match against Southampton came even before a ball had been kicked, with the news that Lucas Leiva was making his return from injury to start a game for the first time since the home fixture against Manchester City.
The Brazilian midfielder was immediately involved, making tackles and interceptions with his usual gusto and, though he overhit a few passes early on, was generally good in possession.
Having Lucas back will be a massive boost for Liverpool and the midfield was visibly improved in shape and balance with him shielding the defence.
It remains to be seen whether he features in Italy midweek, but the 87-minute appearance he made against the Saints will do himself, the manager and the fans the world of good.
Having been treading a fine line for a few weeks now, Luis Suarez finally picked up his fifth booking of the season and as a result will miss the next Premier League fixture.
That will be in a week's time as Liverpool visit West Ham United at Upton Park—and with Fabio Borini still injured, the Reds will face having no senior striker available again.
Brendan Rodgers will presumably turn to Jonjo Shelvey again, after the midfielder played that role in the Europa League against Young Boys previously.
The other option would be to let one of the younger forwards start, with Samed Yesil or Adam Morgan having had the most game time this season out of the possible candidates.
On the other hand, with Liverpool having a tricky and important Europa League tie against Udinese in midweek, Suarez will now almost certainly start that game up front as the Reds bid to qualify from the group.
How many chances do Liverpool need to score? How long has this been going on for?
If ever there were any lingering doubts of whether the Reds needed to spend on attackers capable of finding the back of the net in January, the fixture against Southampton should have dispelled them nicely.
Liverpool had a whopping 23 shots during the match, eight of which were on target and two of which hit the woodwork.
Even the statistics only tell part of the story though as Martin Skrtel, Jose Enrique and Raheem Sterling in particular passed up quality chances to score without even taking a shot in the end.
Sterling should have ended the game as a contest late in the second half with two great chances, but the confidence and quickness of the Reds as a whole in the penalty box needs to be taken up a couple of notches.
This was a game that Liverpool should have won by four or five goals, not been a little nervous in the final 10 minutes in case Southampton hit them with a sucker-punch equaliser.
After some below-par performances from Liverpool captain Steven Gerrard in recent weeks, the fans and the management would have been delighted to see him back to a higher level of performance.
It lasted around 70 minutes or so, after which he was guilty of giving the ball away again and not helping out as much as needed in the defensive third, but for most of the match he was a driving force through the centre and helped construct many of Liverpool's best attacks.
He dovetailed well with Joe Allen in getting forward and exchanged some nice passes with Luis Suarez, but was quickly closed down whenever he looked to shoot.
Corners remain a disappointment from Liverpool, and Gerrard was guilty in this area of not finding a team mate a few times, but overall it was encouraging to see the skipper return to some semblance of good form.
Having spent a few weeks out injured following an indifferent-at-best start to the season, Pepe Reina would have seen there were some calls for reserve 'keeper Brad Jones to continue in goal for Liverpool in his place.
However, since returning to the starting XI Reina has gone on to do what he has always done best—keep clean sheets.
In his four matches in the league, Reina has managed three shutouts, and while he didn't have too much to do in terms of saving shots against Southampton, he was dominant aerially, distributed the ball well and also punched with confidence through a crowded penalty area.
His return to form is as necessary to any success Liverpool have this season as Luis Suarez's goals are, and this latest clean sheet will do his self esteem plenty of good.
Following the win at Anfield it's one from one for victories, and the Reds will go into the match at Upton Park in confidence. They also know they will need to take at least 12 points this month to move significantly up the Premier League table.
Other results this weekend have meant that the Reds move up to 11th, and they are now only two points behind Arsenal, who are just in the top half.
It would be supposed that Arsenal improve their results over the second half of the season, but a top-six spot is very much up for grabs still this season—though Liverpool need to take as many points as possible this month to gain confidence, momentum and placings in the table.
statistics from WhoScored.com