A club-record 13th consecutive home win, courtesy of goals from Rickie Lambert, Guly do Prado, Adam Lallana and Richard Chaplow, made it Saints' best start to a season in 103 years.
Chris Wood pulled one back for City at St Mary's on Sunday but Chris Hughton's side never really looked like breaking their away duck.
These are heady days down at Southampton, who were lying 22nd in League One when Adkins replaced Alan Pardew 12 months ago this week.
With 38 wins from 54 matches in charge the former Scunthorpe boss has turned them into serious contenders for back-to-back promotions and a return to the top flight.
For Blues, however, their Europa League exertions may already be taking their toll.
They have taken just one point from matches following a European outing so far this season, although Hughton was able to make six changes from the side beaten by Braga on Thursday.
Birmingham actually made a bright start in the pouring rain and Wood should have put them ahead within a minute but prodded Jean Beausejour's cross wide.
Moments later Wood's deflected free-kick forced a fine save from Southampton keeper Kelvin Davis.
But Saints were gifted the lead after 10 minutes when Steven Caldwell leant on Lambert in the area and referee Dean Whitestone pointed to the spot.
Lambert, who like Wood hit a hat-trick last weekend, crashed the penalty in off the post for his eighth goal of the season.
They doubled their lead 10 minutes later with a slick move, putting full-back Frazer Richardson through down the right to cross for Brazilian forward Guly to sweep the ball first time past Boaz Myhill.
The third goal, in the 34th minute, was almost a carbon copy with Richardson allowed to reach the by-line before cutting the ball back for Lallana to tuck away.
Wood forced another sharp save from Davis with a free-kick before the break, and the New Zealander made it third time lucky at the start of the second half with a fierce effort from the edge of the area.
Stephen Carr then drove against a post and Davis denied Marlon King as Birmingham briefly threatened an unlikely comeback.
But in the 78th minute Lallana fed substitute Chaplow to tuck away the fourth and keep Adkins' Saints marching on.