Substitute Kelechi Iheanacho equalised for the hosts after a mistake by John Stones gifted Saints' Nathan Redmond the opening goal.
The result left City without a win in five games, equalling the worst run of Pep Guardiola's managerial career, and while they returned to the top of the Premier League, it is only on goal difference from Arsenal and Liverpool.
City could feel hard done to after dominating possession, particularly in the second half, and having a Stones goal controversially ruled out for offside.
Yet after opening the season with 10 successive wins, the intensity does seem to have dropped temporarily.
After Wednesday's heavy loss at Barcelona, there was a feeling City needed to make a statement but that did not happen and they could not rouse themselves enough after a subdued first-half performance.
Sergio Aguero was restored to the front line after his surprise omission in midweek - and some subsequent speculation about his future - while fit-again captain Vincent Kompany made his first league start since April.
City struggled to get going, with promising runs from Aguero, Raheem Sterling and Leroy Sane all coming to nothing.
Fernandinho did whip in a good cross from the right but Sterling was unable to get on the end of it.
Aleksandar Kolarov delivered a superb through ball for Kevin De Bruyne but the Belgian, mostly operating behind Aguero but sometimes drifting left, got the ball stuck under his feet.
City's lack of cutting edge certainly suited Southampton, who struggled to gain any meaningful possession.
When they took the lead it came after a glaring error by Stones, who did not look up as he passed the ball back into the area in the 27th minute
Kompany was not on his wavelength and Redmond pounced, taking the ball wide of Claudio Bravo and smashing home.
The look on Stones' face made clear the horror of his error, which will bring into further focus Guardiola's determination to play out from the back at seemingly all costs.
Stones picked himself up and thought he had made quick amends as he raced in at the far post to tuck home a De Bruyne free-kick
He celebrated what he assumed was the equaliser with gusto but a flag had been raised for what appeared to be offside against Aguero.
The frustration continued for City as Ilkay Gundogan drove wide but the introduction of Iheanacho at half-time brought a change in shape, intensity and atmosphere.
Sterling was enlivened and curled a dangerous ball through the box before City claimed their equaliser after 55 minutes.
Fernandinho picked out Sane with a brilliant crossfield ball and his low cross was neatly tucked in by Iheanacho.
From then on it mainly became a case of Southampton digging in and looking to protect what they had, although Bravo was called upon to make one save from a Charlie Austin drive.
Fraser Forster kept Southampton level by palming away a Gundogan effort before saving Davod Silva's long-range strike.
Aguero threatened with a strong run but was forced wide by Virgil van Dijk and shot across the face of goal.
Jesus Navas was sent on for Kompany late on to provide further attacking impetus but to no avail.
Source: PA