Sadio Mane grabbed a precious opener and Thiago his first for the club in a win that keeps alive Liverpool’s faint hopes of qualifying for the Champions League but, again for Jurgen Klopp’s misfiring strikers, goals were hard to come by.
A team that had 75 goals at this stage last season - and 85 by the time they had played their last four games of the campaign - has scored just 57 this season, an alarming drop-off in productivity.
But at least Spanish midfielder Thiago will remember this game with fondness after he drove into space just outside the Saints area in the 90th minute and clinched the win with a superb piece of placement, into the far corner of the Saints goal.
The game had swung within the space of a breathless minute around the half-hour mark; first when Theo Walcott delivered the perfect cross for Che Adams who only had Alisson to beat 12 yards out.
The Liverpool keeper blocked well, and also saved a follow-up attempt from Nathan Redmond, before his side sped up the other end to take the lead.
Mane skilfully headed in from six yards, having stolen precious inches goal side of his markers, but the goal owed everything to a brilliant cross from Mo Salah who could not have delivered a better ball.
Salah was less impressive moments later when he had the chance to double the lead, a bad touch with only keeper Forster to beat denying his attempt to round the keeper.
And before the opener, Georginio Wijnaldum had been desperately unlucky with an impressive flying header, from Trent Alexander-Arnold’s corner, which clipped the Southampton bar.
Liverpool looked like they might need the cushion of a second goal, with Nathan Tella heading meekly into Alisson’s arms from just six yards, a minute before the break.
But the home side continued to dominate after the restart with Forster, again, saving well from Jota at his near-post and Nat Phillips then heading wide from Alexander-Arnold’s centre.
Salah also had a promising attempt brilliantly blocked by defender Jack Stephens, as he slid across the wet Anfield surface, and the solitary goal looked precarious when Michael Obafemi headed down for team-mate Ibrahima Diallo whose powerful shot from the edge of the area was pushed over, two-handed, by Alisson.
Alisson almost undid that good work with a sloppy pass, straight to Adams, after 76 minutes although the Southampton striker could not get the ball past the keeper from a difficult angle.
Alisson 7; Alexander-Arnold 8, Phillips 7, R Williams 7, Robertson 6; Thiago 7, Fabinho 7, Wijnaldum 7; Salah 7 (Oxlade-Chamberlain 87), Jota 6 (Firmino 79, 6), Mane 7 (Jones 90). Adrian, Tsimikas, Shaqiri, Woodburn, N Williams, Koumetio.
Forster 7; Walker-Peters 7, Bednarek 6, Vestergaard 6, Stephens 7; Walcott 6 (Diallo 65, 6), Ward-Prowse 7, Armstrong 5, Redmond 6; Adams 6 (Djenepo 78, 6), Tella 5 (Obafemi 65, 6). McCarthy, Salisu, Ramsay, N’Lundulu, Ferry, Jankewitz.
K Friend 7