The Croatia international headed in from a corner in the 53rd minute and contributed with a solid display at the back as Liverpool were unable to break down a determined Southampton back line.
Liverpool captain Steven Gerrard twice threatened with free-kicks, but that was the closest the hosts went in a frustrating game for manager Brendan Rodgers after his side’s impressive start to the season.
Liverpool started positively, Daniel Sturridge teeing up Jordan Henderson on the edge of the penalty area, but the Reds midfielder put his shot straight at Southampton goalkeeper Artur Boruc.
Rodgers was incensed with referee Nigel Swarbrick after an early challenge on winger Victor Moses from Saints right-back Nathaniel Clyne went unpunished.
Liverpool were presented with a free-kick in a dangerous position on the edge of the penalty area when Jose Fonte fouled Aspas in the 20th minute. Gerrard curled a shot over the wall from the set-piece, but Boruc scrambled across goal and made a diving one-handed save.
Despite their obvious height advantage at the back, Liverpool conceded from a Lallana corner eight minutes into the second half.
Lovren outmuscled Agger as the pair challenged for a high ball to the back post and the Southampton defender saw his downward header cross the line despite Henderson’s last-ditch attempt to clear.
Other EPL results
Norwich 0-1 Aston Villa
Newcastle 2-3 Hull City
West Brom 3-0 Sunderland
West Ham 2-3 Everton