The pressure was on Nigel Adkins' side following West Ham's 2-1 victory over Nottingham Forest at Upton Park on Saturday.
They made a nightmare start as they found themselves 2-0 down inside 26 minutes and never recovered as Nigel Pearson celebrated a winning return to Southampton - having been manager for three months in 2008 - with Leicester triumphant for only the second time in eight league games.
Leicester took the lead in the 15th minute when former Portsmouth striker Nugent cut in from the left and curled a fine 20-yard effort past the despairing dive of goalkeeper Kelvin Davis.
They doubled their advantage 11 minutes later, defender Mills scoring against the club where he began his career with a powerful stooping header.
Paul Konchesky hit a post in the second half but Leicester still had enough to secure their first win at St Mary's and register the double over Saints having been the first team to beat them this season with a 3-2 home success in August.
Jermaine Beckford, high on confidence following his hat-trick in Leicester's 4-0 home FA Cup third-round replay win over Nottingham Forest last Tuesday, fired wide from 12 yards inside a minute before David Connolly did likewise at the other end as both sides made a quick start.
After Beckford blazed another shot well wide from distance, Connolly forced Kasper Schmeichel into action, although his 20-yard strike was comfortable for the Foxes goalkeeper.
Nugent nudged the visitors ahead with a splendid finish, his ninth goal of the season, and then dragged another effort wide as Leicester continued to cause Southampton problems.
It was 2-0 in the 26th minute. Sean St. Ledger picked up the ball on the left and delivered an inch-perfect cross for fellow defender Mills to head home his first goal for the club - his last coming for Reading in last season's play-off final defeat to Cardiff.
Southampton were struggling to create anything threatening offensively, the closest they came was when Dean Hammond headed a Dan Harding free-kick across the face of goal.
Jack Cork then fired over when well-placed four minutes before the break after good work from Morgan Schneiderlin.
Shortly after the restart Nugent curled a shot wide as Leicester looked for a third, but Southampton came close to pulling one back in the 53rd minute, Schmeichel doing well to keep out Hammond's header at the back post.
Brazilian striker Guly Do Prado, with 11 goals this season, failed to find the execution on his curling effort as the home side's frustrations continued.
Leicester so nearly added a third in the 62nd minute, Konchesky's left-footed free-kick hitting a post, with Davis well beaten, before rolling across the face of goal and to safety.
Davis saved from Beckford and Foxes substitute Nathan Delfouneso, signed today on loan from Aston Villa, blazed over while home sub Lee Holmes was wastefully wide late on to sum up Saints' night.