Jurgen Klopp’s side knew defeat would hand the title to Manchester City – while even a draw would effectively end the challenge because of their inferior goal difference.
And it looked as if Liverpool might have a struggle on their hands when Nathan Redmond gave Southampton a 13th-minute lead with a curling right-foot shot beyond Alisson.
Liverpool, with nine changes from the side that won the FA Cup by beating Chelsea on penalties at Wembley on Saturday, once again showed their resilience and reserves of strength as Takumi Minamino levelled before half-time with a thumping drive against the club where he spent a spell on loan last season.
The pressure built after the break and Liverpool took a deserved lead after 67 minutes when Joel Matip sent an instinctive looping header over Saints’ keeper Alex McCarthy.
City will still retain their title with victory over Aston Villa at Etihad Stadium but Liverpool have pushed them all the way again and ensured the fight will go down to the wire.