Jurgen Klopp took a gamble with nine changes at St Mary's after Liverpool defeated Chelsea on penalties in a knife-edged FA Cup final just three days earlier.
Despite effectively fielding a reserve team and trailing to Nathan Redmond's early strike, Liverpool hit back through goals from Takumi Minamino and Joel Matip.
The Reds are just one point behind leaders Manchester City, with both teams having one game left.
A title race for the ages will go City's way if they win against Aston Villa at the Etihad Stadium on Sunday.
Klopp insisted at the weekend that he does not expect City to drop points against Villa.
But Liverpool would be crowned champions for the second time in three seasons if they beat Wolves at Anfield and City fail to win.
Klopp's side will be expected to do their part of the equation against Wolves, especially now their refreshed key players can return to the team.
Sadio Mane, Luis Diaz, Andrew Robertson, Thiago Alcantara and Trent Alexander-Arnold were among those left out against Southampton, while Mohamed Salah and Virgil van Dijk were sidelined with injuries suffered at Wembley.
City boss Pep Guardiola said he planned to watch the game on television and if he tuned in, it would have made for frustrating viewing as Southampton squandered the lead.
But it was Riyad Mahrez's missed penalty in the final minutes of City's 2-2 draw at West Ham on Sunday which had given Liverpool renewed hope of catching the leaders.
And the Reds, hoping to become the first English club to win all four major trophies in one season, will settle their history bid in the last two games of their incredible, marathon campaign.
First, Liverpool will try to avoid a repeat of 2019, when they beat Wolves on the last day but were still pipped to the title by City.
Then they head to Paris to face Real Madrid in the Champions League final on 28 May