The Royals had their chances in the early stages but fell behind to Jay Rodriguez's 34th minute strike and Southampton never looked back as they sealed another impressive win.
Adam Lallana netted a second goal in the 72nd minute for Saints, who are now seven points clear of the drop zone, while Reading's battle for survival now appears doomed as they remain seven points adrift of safety with just six games to play.
Adkins, sacked by Southampton in January, was given a good reception by the fans of both teams as he acknowledged the crowd, and it was his new side who made the brighter start.
Sean Morrison headed over in the first few minutes after beating his marker to a Danny Guthrie free-kick, before Adam Le Fondre spurned a glorious opportunity when the ball broke for him in the box and he blazed a volley horribly over from close range.
Reading continued to apply pressure and had a confident penalty appeal turned down midway through the first half as referee Mike Jones ruled that Hal Robson-Kanu had been tackled cleanly by Jos Hooiveld, while Artur Boruc made a scrambling save down to his right to keep out Adrian Mariappa's header.
However, the game turned in the 34th minute as Rodriguez latched on to a Rickie Lambert pass just before it could be intercepted by the onrushing Adam Federici, and his determination was rewarded as the ball ricocheted into the net.
Reading appeared deflated by the sudden setback and it could have got worse for them before half-time as Rodriguez crashed an effort against the woodwork and then had a shot stopped by Federici, with Gaston Ramirez surprisingly lacking composure as he steered the rebound wide.
Hope Akpan was replaced by Mikele Leigertwood at the interval as Adkins tried to find a way back into the game, but Southampton remained in control as they soaked up Reading possession and threatened on the counter-attack.
Federici was again called into action to prevent Steven Davis from doubling Southampton's lead following a terrific ball by Lambert, who minutes later was just unable to reach Rodriguez's cross to the back post at the end of a flowing move.
Saints eventually managed to double their lead in the 72nd minute when Lallana was released by a sublime pass from Rodriguez and finished calmly past Federici from the edge of the area.
Reading were nearly given a lifeline when Boruc came perilously close to carrying the ball over his own line as he held a Le Fondre header, but there were few other alarms for Southampton as they held on for an important victory.