Liverpool fell behind inside two minutes, with the Reds caught off-guard from a clever free-kick by James Ward-Prowse.
Liverpool had plenty of the ball but failed to muster up any chances, with the Reds severely lacking in creativity against a staunch Saints defence.
The Reds went close through a Salah header just before half-time after good work from Sadio Mane, but there was little else to shout about during the second half.
Liverpool controlled the ball for large spells but couldn't find a breakthrough, with the attack looking short on ideas.
Mane had the visitors' first effort on target in the 75th minute but scuffed his low effort before having another chance in added time, but it wasn't to be the champions.
The result means the Reds remain level on points with Man United, having played a game more, whilst Leicester sit just one point behind in third.