The visitors led when John Stones’ sloppy pass allowed Nathan Redmond to round Claudio Bravo and slot in.
City improved after being booed off by some home fans at the break, equalising when half-time substitute Kelechi Iheanacho prodded in Leroy Sane’s low cross.
Pep Guardiola’s side controlled the second half as they searched for a winner, but Saints keeper Fraser Forster produced splendid saves to deny Ilkay Gundogan and David Silva.
City’s inability to grab a second goal means ex-Barcelona and Bayern Munich boss Guardiola has failed to win in five successive matches for only the second time in his managerial career.
However, the point was still enough to lift the Blues back above Arsenal and Liverpool to the Premier League summit.
Southampton stay eighth after extending their unbeaten league run to a fifth game.
City stutter… again
City’s recent struggles are barely believable after the swaggering start they made to the season, when they won all of Guardiola’s opening 10 matches.
The former Spain international had been forced to defend his tacticsfollowing Wednesday’s 4-0 Champions League defeat at his former club Barcelona, which came after their first loss of the season at Tottenham and the subsequent home draw against Everton.
But there were signs of the home support becoming frustrated with his team’s build-from-the-back approach, not least when many could be heard jeering their team off at the break after Stones’ error.
City lacked aggression and tempo in the opening 45 minutes, allowing an organised Southampton side to contain them and then burst forward on the break.
Guardiola had to act – and he did that decisively at the break.
Off came Kevin de Bruyne – City’s stand-out performer this season – with young striker Iheanacho introduced in his place.
As a result, City had much more purpose and drive, typified by the desire showed by Iheanacho to beat Saints defender Virgil van Dijk to Sane’s cross and prod in the equaliser.
Stones not quite rolling
Stones is the only player to feature in every match of Guardiola’s reign following his £47.5m summer move from Everton, impressing his new manager with his composure and ability to play out comfortably from the back.
But critics have argued the England international is guilty of over-playing, leaving himself open to making mistakes. They were proved right on both counts when he gifted Southampton the lead.
After receiving the ball just outside his own area, Stones tried to pass inside to returning skipper Vincent Kompany – instead playing it behind his captain and straight to Redmond.