Jurgen Klopp’s Liverpool side, for whom this was a second league loss of the season, remain top of the table on goal difference but have taken only two points from the past nine available.
Both Manchester United and Manchester City will leapfrog the reigning champions if they win their games in hand.
Southampton’s first win in five Premier League games sees them climb to sixth and brought an emotional response from manager Ralph Hasenhuttl, who sank to his knees to celebrate taking points against a side led by Klopp for the first time.
And the hosts were good value for their victory, forcing the pace early on against an unfamiliar Reds backline containing Jordan Henderson, and then defending resolutely as the visitors poured forward after the break.
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While Liverpool can point to the huge void at the heart of their defence and several injured stars, it should also be acknowledged that Southampton began this contest without several key performers.
Goalkeeper Alex McCarthy’s positive coronavirus test meant Fraser Forster came in for a first Premier League home appearance since December 2017.
And with Jannik Vestergaard, Oriol Romeu and Che Adams also injured, Hasenhuttl could ill afford to see Moussa Djenepo limp off after 32 minutes, during which he had caused Trent Alexander-Arnold several problems down the left.
Initially at least, they continued to play in their normal style, trying to retain possession and work the ball into promising positions out wide.
Nathan Tella’s curling, right-foot shot, after Ings had expertly cushioned the ball into his path, almost brought the reward of a second goal.
However, after the break it was very much a rearguard action from the Saints, with Kyle Walker-Peters, Jan Bednarek and Jack Stephens making seven clearances each to repel wave after wave of Liverpool attacks.
That resilience was underlined by restricting the Reds to just one shot on target – a Sadio Mane effort in the 75th minute.