Goals from Jay Rodriquez after 34 minutes and Adam Lallana after 72, both following poor Reading defending, condemned the Biscuitmen to a seventh successive league defeat.
Adkins, replaced as Southampton boss by Argentine Mauricio Pochettino in January, has seen his side lose his three matches in charge.
Southampton thoroughly deserved the win, but almost conceded a late goal when goalkeeper Artur Boruc floundered as he caught a header from Adam Le Fondre and appeared to carry the ball over the line. He did just enough to keep it out, however.
The victory took Southampton, who have improved under Pochettino, up to 11th in the standings and virtually sure of avoiding relegation.
Reading remained 20th, level on 23 points with Queens Park Rangers and seven points from safety with only six matches remaining.
In the day's other Premier League games, Norwich City play Swansea City, Stoke City face Aston Villa and West Bromwich Albion host Arsenal. — Reuters