McInnes, who took over at Ashton Gate last month following the dismissal of Keith Millen, saw his side extend their unbeaten run to five matches courtesy of strikes from Albert Adomah and Nicky Maynard on Saturday.
Adomah followed up his initial effort after 53 minutes to secure all three points for the Robins, who dominated long periods of play against their in-form guests.
And Maynard capped another impressive personal display with the second goal six minutes from time to secure their best result of the season.
Maynard, Marvin Elliott, Kalifa Cisse and Adomah all had good chances for the home side, while Adam Lallana and Steve De Ridder wasted Saints’ clearest openings during a lively encounter.
But in the end it was McInnes’ side who came out on top.
Southampton suffered an early blow when Richard Chaplow was forced off with an injury, with Morgan Schneiderlin replacing him after just seven minutes, before the Saints had the first real opportunity of the match eight minutes later.
In-form Lallana made veteran City goalkeeper David James produce a decent save low down, as the away side enjoyed the better of possession and territory in the early stages.
The home side steadily found their feet and began to test their table-topping guests.
Maynard fired a shot well over the crossbar after 23 minutes when he was set up following good work from Adomah and the Ghanaian tried his luck from distance without success, before Saints stopper Kelvin Davis almost spilt Ryan McGivern’s cross into his own net.
The keeper cut a relieved figure as the ball dribbled gently wide of the post to spare his blushes.
Adomah continued to cause the Southampton back four problems and his neat pass set up Marvin Elliott after 38 minutes, only for the midfielder to poke a timid effort straight at Davis.
The away keeper was much the busier as the game approached halfway, saving from Cisse, and both Maynard and Stephen Pearson wasted good opportunities as the sides went into half-time locked at 0-0.
City started the second period with the same intensity that they finished the first and they were duly rewarded with the lead three minutes after the interval.
The irresistible Adomah wriggled free of his marker to fire a deflected effort into the back of the net after Davis had saved his initial shot.
Southampton went close to responding immediately through Jose Fonte, but the defender put his effort wide from a free-kick.
And Saints striker Guly Do Prado passed up a glorious chance from six yards out moments later as the visitors finally rediscovered their rhythm.
Substitute Martyn Woolford provided some respite for the City defensive unit, as he saw his effort well saved by Davis, but the hosts were soon on the back foot again.
De Ridder wasted a good chance for Southampton, blazing over from 18 yards when well set.
And the Saints sub was left to rue his miss moments later when Maynard battled into the area to beat Davis with a looping, deflected effort.