The 31-year-old, who returned to City’s starting line-up to make just his fifth appearance of the season, sent the visitors on their way to victory at St. Mary’s in the 56th minute, rising highest to head David Silva’s corner past Fraser Forster.
The points were then made safe in the 77th minute with Leroy Sane finishing off a swift counter-attacking move before Sergio Aguero (80) completed the scoring on a comfortable afternoon for the visitors.
Victory moves City up into third ahead of Liverpool, who play West Brom on Super Sunday, and seven points clear of Everton in fifth and Manchester United in sixth, as Jose Mourinho’s side host Chelsea on Sunday, live on Sky Sports.
Meanwhile, Southampton, who saw a three-game unbeaten run come to an end, stay in ninth.
Manolo Gabbiadini returned from injury to start his first match in just under a month, while Kompany’s inclusion was the standout news as Guardiola made another four changes to the side that beat Hull last time out.
City started on the front foot with Clichy creating an opening for Aguero at the far post but the striker fired an awkward volley wide at the far post.
Aguero was back in the action again minutes later, bringing the ball down in the penalty area before firing a shot wide of the far post.
City were dominating the ball with Southampton sitting deep, but they finally showed their attacking intent in the 15th minute when Nathan Redmond’s pass released Gabbiadini on the right. The striker pulled the ball back for Tadic on the penalty spot but the Serbia international blazed the ball high over the crossbar.
The visitors had a clear chance of their own in the 37th minute when Aguero produced a brilliant change of pace to get to the byline before picking out Silva at the far post, but the Spanish midfielder failed to hit the target with the goal at his mercy.
A minute later came the talking point of the first half when Leroy Sane strode through on goal before attempting to go around Fraser Forster. Sane went to ground after contact with Forster but the England goalkeeper appeared to get a significant touch on the ball which was spotted by referee Neil Swarbrick.
After the break, Forster got a firmer hand onto a stinging drive from Jesus Navas to palm the ball over the crossbar.
However, from the resulting corner, swung in by Silva, Kompany got his head to the ball first and Forster was unable to prevent it bouncing into the net.
Claudio Bravo, who had failed to stop any of the last seven shots on target he had faced, then caught a header from Maya Yoshida – the first save he had made since January 2.
City then promptly wrapped up the win with two goals in three minutes. First, Silva’s through-ball sent De Bruyne through and he squared for Sane to sweep past Forster for his ninth of the season.
Then, in the 80th minute, De Bruyne chipped the ball into the Saints six-yard box and Aguero nodded home at the far post to seal an ultimately comfortable, and potentially crucial, victory.
