Luis Suarez set Liverpool on the way with the opener in the first half and substitute Raheem Sterling added a second in the second half with his first touch after coming on.
Steven Gerrard put the seal on a perfect evening for Brendan Rodgers' side with a third from the penalty spot in the closing seconds.
The defeat was harsh on Southampton as they pushed Liverpool back for long periods and went close to scoring on several occasions.
Liverpool nearly opened their account on seven minutes as Daniel Sturridge led a a break from the visitors and tried to pick out Suarez for a tap in, but Jose Fonte got back brilliantly to clear the ball in front of the Uruguayan.
The visitors did break the deadlock on 16 minutes with Suarez celebrating his 100th Premier League appearance in style with his 24th goal of the season.
The goal was somewhat fortuitous as Southampton's defence failed to clear their lines and the ball diverted off Fonte into the path of Suarez who slotted his first-time shot past Artur Boruc.
Southampton reacted positively to going behind and Luke Shaw created a chance for Rickie Lambert on 26 minutes, but the striker drilled his shot wide of the target.
The home side were inches away from drawing level on 32 minutes when Lambert knocked down the ball into the path of Lallana inside the six-yard box and he was unlucky to see his effort come back off the post.
Southampton were going forward at every opportunity and Lallana and Rodriguez both saw efforts fail to hit the target as they pushed for an equaliser.
Southampton continued to call the tune before half-time and Simon Mignolet came to Liverpool's rescue two minutes before the interval as he got down well to keep out Jay Rodriguez's effort with a strong hand after Lambert had cleverly dummied Shaw's pass inside the box.
Southampton picked up where they left off at the start of the second half as they pushed Liverpool back, but Liverpool caught them on 58 minutes with Sterling netting their second goal.
Suarez spun Lovren from Gerrard's pass and he cut the ball back for Sterling to slot home past Boruc just 80 seconds after entering the action.
Sturridge had a chance to continue his rich vein of form in front of goal on 69 minutes when he latched onto Suarez's pass to round Boruc, but from a tight angle he was unable to direct his effort on target.
Gerrard went close to scoring on 73 minutes when his long-range effort was tipped round the post by Boruc.
Liverpool added a third deep into injury time when Suarez was felled inside the box by Jose Fonte and Gerrard drove home from the spot to maintain their bid for a title challenge.