Leroy Sane and Sergio Aguero were also on target as City cemented their place in the Premier League's top four.
Manchester City faced a tough test against Southampton, but after creating many chances in the first half, the Sky Blues scored the goals in the second half to pick up three vital points in the Premier League table.
MAN CITY: Bravo 5, Navas 3, Kompany 13, Otamendi 8, Clichy 8, Fernandinho 3, Toure 3, De Bruyne 12, Silva 5, Sane 8, Aguero 8.
The result lifts the Citizens into third place above Liverpool, while they are seven points behind Tottenham, who occupy second spot.
"When something like this happens I feel like I'm giving something back to the team and the fans and that's what you see in those moments".
"I love him for how he plays and because we play together in the Selecao and we did at the Rio Olympic Games".
Pep Guardiola is gearing up for a semi-final - and a final - after Manchester City swept aside Southampton 3-0.
Neymar set to miss crucial El Clasico clash
He was given a yellow card for "obstructing a free-kick" when he bent over to tie the laces of his shoes. Los Blancos are now three points clear of their fierce rivals and have one game in hand.
Sane will be eligible for the Young Player of the Year award for another two years and if he continues his impressive rise at City, it will be hard for anyone to stop him winning it in those seasons to come. "I would have been done and dusted if I needed every single time to get back in and time to adapt", Kompany said after only his eighth appearance of a frustrating stop-start season. The team try to have possession and to give always a good response on the game.
"It's ups and downs in football, but ultimately what gets you up is that you keep looking towards your objective".
"I don't complain and (I) just carry on".
Manchester City manager Pep Guardiola has said he will be watching today's match between Manchester United and Chelsea at Old Trafford with a professional interest rather than willing the Londoners to win.
Despite spending heavily in recent seasons, City's title aspirations have been hampered by an inability to build a consistent, reliable central defensive partnership in Kompany's absence.
With 20 minutes to go Yoshida had the golden chance to make up for allowing Kompany to rise above him and score when he found space at the far post, only to head straight down into the hands of under-fire City stopper, Bravo.
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