Goals by Raheem Sterling, Sergio Aguero, David Silva and Leroy Sane helped City gain maximum points to stay on top of the championship standings.
City raced to a 3-0 lead in the first 18 minutes before Danny Ings pulled one back for Southampton.
City made it four goals in the first half through a strike by Sergio Aguero.
Sterling and Sane completed the rout by adding two more goals in the second half.
City manager Pep Guardiola was all praise for Sterling.
“He is in incredible form, he is sharp, fast, clever, fighting, decisive, he can play both sides and can play in the middle and receive the ball between the lines and commit the centre-backs with a lot of aggression,” Guardiola said.
City’s title rivals Chelsea defeated Crystal Palace 3-1 thanks to a brace by Alvaro Morata.
With this win, Chelsea moved into second place in the Premier League behind Manchester City.
Speaking of Morata, Chelsea manager said the Spanish striker has a great potential.
“He is a little bit fragile from the mental point of view, but he is very young I think he can improve very fast. I think also Alvaro has a very great potential, physical potential, technical potential, so he has to improve more,” Sarri said.