The Blues took the lead when Eden Hazard capitalised on poor marking before cutting inside Steven Davis and powering a shot through the legs of keeper Fraser Forster.
Southampton had plenty of the ball but could not find a way through a well-drilled Chelsea, who looked the more threatening and went close when strikes from Hazard and Diego Costa were saved.
Costa, however, beat Forster at full stretch with a wonderful curled effort from 22 yards.
Victory was Chelsea's fourth in a row in the league - a feat they last achieved in April 2015 - and put them one point behind Manchester City, Arsenal and Liverpool.
Source: BBC Sports