Agger header enough against Saints
The Denmark international powered home a header just before half-time, only his fifth in 133 Premier League appearances, after a host of chances had gone begging.
In doing so he helped the Reds to only their third home win of the season and back-to-back league wins at Anfield for the first time since September 2011.
Jonjo Shelvey bobbled straight at goalkeeper Paulo Gazzaniga, Glen Johnson flicked Luis Suarez's pass across the face of goal, Steven Gerrard had a shot charged down and then fired wide after a quickly-taken free-kick to Suarez as Liverpool started strongly.
Gazzaniga denied both Shelvey and Suarez, who made justifiable claims he had been pulled back by Jack Cork, before the Uruguay international latched onto Jose Reina's long kick and beat the goalkeeper only for Maya Yoshida to clear the ball for a corner.
When Shelvey smashed an angled shot past the goalkeeper but back off the inside of the far post it appeared luck was not on their side.
However, it took a double-dose of Uruguayan intervention to eventually help break the deadlock two minutes before the break.
Saints' South American summer signing Gaston Ramirez flattened international team-mate Suarez on the edge of the penalty area and although the Reds striker crashed his free-kick onto the crossbar it rebounded to Johnson. His cross into the penalty area was met by Agger who planted a header into the top corner from 10 yards.
Jose Enrique saw his drilled half-volley from the left of the area batted away by Gazzaniga and such was Liverpool's desperation to score the second and give themselves some breathing space Suarez tried to punch in Gerrard's cross.
Suarez flashed a left-footed shot just wide in added time but in the end Agger's goal proved just enough to ensure they crept closer to the top four, which manager Brendan Rodgers insists remains a possibility.