A clinical, professional and solid display secured a vital victory for the visitors, lifting them to third in the Premier League table.
City dominated proceedings and netted three second half goals to claim the triumph – one of which was an excellent, well-worked breakaway goal to kill any hopes of a Saints comeback.
The Blues started brightly and Aguero, seeking his 29th of the season, had three sights of goal within the opening eight minutes.
Sane and David Silva combined well to release Gael Clichy down the left and the Frenchman whipped in for the Argentine, who could not direct his effort on target.
The striker then dragged a shot wide, having been played through by Kevin De Bruyne, before volleying a pinpoint corner off-target.
Southampton’s first chance of the afternoon arrived on 13 minutes, as Manolo Gabbiadini pulled back for Tadic, who blazed over.
The Blues dominated the opening half hour, while the hosts – content to let City take control – grew into the game.
There was a flurry of activity in the final ten minutes of the half as Steven Davis headed over at one end and Silva slid into the side-netting at the other.
PFA Young Player of the Year nominee Sane was then denied what looked a clear penalty, as he was upended in his attempts to round Fraser Forster in the Southampton goal. Replays suggested the Saints man had managed the faintest touch of the ball but his contact with the German winger was far more obvious.
Silva went in search of his 50th City goal but drilled the ball the wrong side of the post in the last major action of the half.
The early stages of the second half produced a more even affair. Yaya Toure forced Forster into the first save of the game with a curling effort while James Ward-Prowse lifted a free-kick over the bar.
City regained control though and Jesus Navas went close with a driven effort which Forster tipped over. From the resulting corner, City broke the deadlock as Kompany rose highest to head Silva’s delivery home.
The celebrations that ensued depicted just how much the strike meant to the skipper, who raced to the travelling army to share the joy.
The Belgian almost doubled his tally moments later from close range but this time, his shot was blocked.
Aguero almost wrote his name onto the scoresheet at the fourth attempt, following lovely build-up play between Silva, Toure, Navas and De Bruyne – but was also thwarted.
Claudio Bravo then prevented Maya Yoshida from levelling the score, collecting the centre-back’s backpost header and City extended their advantage minutes later.
De Bruyne regained possession in midfield and found Aguero, who immediately played to Silva. The Spaniard then sent De Bruyne clear and the Belgian squared for the accompanying Sane who slotted home.
Victory was sealed on 77 minutes as Aguero continued his excellent form, heading in at the backpost from De Bruyne’s floated cross to cap a superb evening.
Courtesy of his two assists, the midfielder leads the Premier League list for the season with 13.
11 - Manchester City have won more away games this season than they have in any other top flight campaign. Legs. pic.twitter.com/j7ffvmjoj0— OptaJoe (@OptaJoe) April 15, 2017
Matchday App Man of the Match
A win, a goal, a clean sheet and a full game definitely deserves to be celebrated and it was Kompany, who enjoyed a perfect afternoon, who took the plaudits.
Kompany, Nicolas Otamendi, Fernandinho and De Bruyne returned to the starting XI in place of John Stones, Aleks Kolarov, Raheem Sterling and Fabian Delph.
Stones, Delph, Bacary Sagna, Gabriel Jesus and Ilkay Gundogan missed out through injury, while Nolito was rested.
What it means?
City leapfrog Liverpool into third with 64 points, whilst distancing themselves from Everton (fifth), Man United (sixth) and Arsenal (seventh).
A pivotal week lies ahead as City travel to Wembley to face Arsenal on Sunday 23 April at 3pm, seeking a place in the FA Cup final.
The Blues are back in Premier League action on Thursday 27 April with the Manchester derby (8pm).