Dejan Lovren's second-half header proved to be enough to give Southampton all three points as they inflicted the first defeat of the campaign on Brendan Rodgers' side.
Southampton were the last side to beat Liverpool prior to kick-off when they won at St Mary's last March and they repeated the trick to secure a famous win for Mauricio Pochettino's side.
Liverpool created the first opening of the game on three minutes when Daniel Sturridge teed up Jordan Henderson on the edge of the box, but his curling effort was comfortably saved by Artur Boruc.
Southampton were more than holding their own and they looked dangerous every time they got forward, but all too often their final ball broke down on the edge of the box.
Liverpool went close to breaking the deadlock on 22 minutes when Steven Gerrard saw his brilliant curling free-kick from 25 yards spectacularly kept out by a flying Boruc at full stretch.
Four minutes later, former Liverpool trainee Rickie Lambert had a sight of goal when the home side failed to clear their lines inside the box and the ball dropped to the Southampton striker inside the six-yard area, but he mis-timed his left-footed volley and the ball looped into the arms of the grateful Simon Mignolet.
Liverpool thought they had won a penalty on 33 minutes when Sturridge went down on the edge of the box under a challenge from Lovren, but much to the annoyance of the home side referee Neil Swarbrick waved away their appeals.
Victor Moses looked lively on his home debut for Liverpool in the first half and he went close eight minutes before the break after he burst into the box past Jose Fonte, but Boruc stood up well to keep out his prodded effort.
Liverpool almost gifted Southampton a goal two minutes into the second half when Mignolet overplayed with the ball and Nathaniel Clyne played Adam Lallana in on goal, but the goalkeeper redeemed himself to keep out his shot.
Southampton broke the deadlock on 53 minutes when Lovren lost Daniel Agger to head home Lallana's corner with Gerrard just unable to keep the effort out on the line.
Liverpool tried to rally themselves and on the hour mark Gerrard saw a powerful free-kick from the edge of the box well kept out by Boruc.
Southampton almost grabbed a second goal on 67 minutes only to be denied by a wonderful triple save by Mignolet.
Firstly Mignolet kept out Luke Shaw's shot before producing fine reactions to block the deflection off Mamadou Sakho and then finally getting back to his feet to punch the ball away from substitute Steve Davis with the goal at his mercy.
Liverpool huffed and puffed in the closing stages in a bid to get back into the game, but Southampton's defence held firm to earn a memorable win on Merseyside.