The champions were second best for large periods of the game at St Mary's and fell behind in just the seventh minute when Jason Puncheon tucked away the rebound from Rickie Lambert's strike.
City then became their own worst enemy as Steve Davis doubled the home side's lead after goalkeeper Joe Hart allowed Lambert's shot to squirm through his hands.
Edin Dzeko reduced the arrears before half-time but a Gareth Barry own goal early in the second half secured a first win for Saints' boss Pochettino.
"I'm very proud and very happy for the team, who deserved the victory," he said.
"I'm very happy for all the people who work with Southampton and for all the people here at St Mary's today, it has been an incredible day."