The victory moves Liverpool into sixth and Brendan Rodgers' side is now two points behind Manchester United, who still occupies the fourth and final Champions League position, despite losing 2-1 at Swansea on Saturday.
A brilliant long-range strike from Philippe Coutinho put Liverpool ahead after three minutes, with the Brazil international's effort beating Southampton goalkeeper Fraser Forster from 25 yards and going in off the crossbar.
Southampton had most of the possession in the second half but could not break down Liverpool's stern defence.
And Raheem Sterling secured the win in the 73rd, lashing in from the edge of the area after Matt Targett failed to clear Alberto Moreno's cross.
"It is an excellent win, defensively we were very strong,' Rodgers said, before refusing to be drawn on his side's chances of usurping United. "It is just going to be small steps for us. We have organised the team in a different way and we have been playing two or three times a week now for the last four months and today was a huge win."
Liverpool overtook Tottenham in the table after Mauricio Pochettino's side came from two goals down to draw 2-2 against West Ham at White Hart Lane.
Cheikhou Kouyate and Diafra Sakho had put West Ham 2-0 ahead before Danny Rose's mis-hit from distance went in after 81 minutes and Tottneham were suddenly galvanized.
Harry Kane won a penalty after going down from a challenge by Alex Song but West Ham goalkeeper Adrian saved the spot kick in the sixth minute of added time.
But Kane was first to the rebound and duly converted with the game's last kick.
"I think we showed character — that's the most important thing," Pochettino said. "Going into the last 10 minutes at 2-0 down, to finish the game 2-2 is something to be proud of."
Elsewhere, Everton was held 2-2 at home to bottom club Leicester.
Steven Naismith put the host ahead in the 57th, but two goals in seven minutes from David Nugent and Esteban Cambiasso stunned Goodison Park.
But Everton equalized two minutes from the end, as defender Mathew Upson turned Christian Atsu's cross into his own net.