The Croatia international struck in the 54th minute to end Liverpool's 12-match unbeaten league run spanning this season and last. But Southampton - the last team to defeat the Anfield club, in March - may not have won 1-0 had referee Neil Swarbrick seen the defender bring down Daniel Sturridge in the first half.
That incident aside, however, Liverpool did not create nearly enough chances for a team which began the day top of the table.
On this evidence the return of the watching Luis Suarez, sitting out the final game of his 10-match ban for biting Chelsea's Branislav Ivanovic in April, will come not a moment too soon.
It was a view shared by Liverpool manager Brendan Rodgers, who said: "I think that is the big positive from today, the fact he is back and is available from next week.
"Sometimes players like him can make the difference so it is a real boost to have him back from Wednesday onwards. He has been playing games behind closed doors and doing a lot of specific work with the conditioning team."
Suarez is likely to return for the midweek Capital One Cup tie at Manchester United, so this was perhaps Iago Aspas' last real chance to impress following his summer move from Celta Vigo.
The Spaniard scored 12 goals last season but has yet to score in five league games for his new club. He was replaced by Raheem Sterling at half-time.
Steven Gerrard had tested Artur Boruc with a first-half free-kick and Lovren - unseen - brought down Sturridge, but that was as much as Liverpool managed to muster.
"We are very disappointed. We never got going from the off, it was a bit lethargic and technically we were short," Rodgers added. "We conceded possession poorly, then ended up conceding the corner and to lose a goal like what with so many defensive-minded players was criminal."
Rodgers' defensive line-up consisted of four centre-halves - arguably the strongest area of his squad - with Kolo Toure on the right and Mamadou Sakho on the left, flanking the returning Daniel Agger and Martin Skrtel, both later replaced in a points salvage attempt.
"Over 90 minutes we were superior and were able to capitalise on the chances we created," said Southampton manager Mauricio Pochettino, most notably of Lovren, who beat Agger to Adam Lallana's corner to head down and past Gerrard on the goal-line for the decisive strike.