Guly do Prado was the star performer in a Jekyll and Hyde display from the table-topping Saints, who threw away a two-goal lead before sealing the points late on at the Ricoh Arena.
The Brazilian midfielder provided carefully-crafted assists for Richard Chaplow and Adam Lallana in the first half before netting his side's third goal after the break.
City had bravely fought back before being undone by two late goals but the defeat leaves them fighting for their lives in the bottom three.
There were early warning signs for Andy Thorn's side as Chaplow burst down the right early on but failed to take advantage of a good position as his cross was easily cleared.
Morgan Schneiderlin then fired in a long-range effort which had Joe Murphy scampering across his goal but it went narrowly wide.
In a rare attack for the hosts, Lukas Jutkiewicz fired a left-footed shot over the bar from 12 yards.
Nigel Adkins' men soon reasserted their authority and Chaplow had another chance to break the deadlock when he latched on to Rickie Lambert's knock-down, but the midfielder's shot found the side-netting.
After Gary McSheffrey skewed a shot wide, the visitors finally finally got their deserved opener on 34 minutes. Guly delivered from the left for the industrious Chaplow to sweep home from 12 yards.
It could, and perhaps should, have been two moments later when Lambert brilliantly controlled and laid it off for Daniel Fox, whose delivery found Lallana but his header was straight at Murphy.
Lallana made amends when he notched his sixth of the season six minutes before the interval. Guly was the architect once more, skipping down the left before looking up to find Lallana in space and he made no mistake from six yards.
It could have been Thorn's half-time team-talk or the visitors' failure to switch on at the start of the second half, but it was game on as City pulled a goal back within two minutes of the restart.
Sammy Clingan raced to the by-line and squared the ball for Jutkiewicz, who rattled in his sixth of the campaign.
The resurgent hosts turned the screw on their high-flying opponents as Clingan tried his luck with a swerving long-range drive which went just wide.
Celtic loanee Jos Hooiveld spurned a chance to alleviate the pressure when he tamely headed over from Lambert's pinpoint set-piece delivery.
And they were made to pay in the 70th minute when a deflected shot fell kindly for Coventry substitute Clive Platt, who took it past Kelvin Davis and rolled in the leveller.
Southampton, however, were not done and they regrouped to take control of the game once more with a third goal in the 77th minute. Fox was the provider this time, whipping in a stunning cross for Guly to guide a header into the bottom corner.
The visitors made sure of their 11th win of the season, and first at the Ricoh Arena, when Steve de Ridder converted from the heart of the penalty area with just five minutes remaining.
Saints' points return after 16 games is the best they have achieved for 90 years and Adkins side are looking every inch promotion candidates.
