Chester struck twice in the second half as they came from behind to take maximum points at the Pure Stadium on Boxing Day.
It was Southport’s first defeat in four games in the Vanarama National League North, as the visitors overtake them in the tightly-packed play-off places.
Ryan Astles put the Port in front but Chester deserved their win, having been the stronger team from the start and controlled large periods of the game.
Liam Watson’s side have a chance to bounce back quickly when they visit Altrincham on Saturday before facing Chester again on New Year’s Day.
The visitors were out of the traps quickly, hitting the woodwork twice and bringing a save from goalkeeper Charlie Albinson in the opening stages.
A cross from Joel Taylor drafted against the Port post before Dean Winnard made a block from the rebound. Having worked his way cleverly into space on the edge of the area, George Glendon also sent a shot against the upright as the visitors enjoyed the better of the early play.
Glendon showed his ability to pick up dangerous areas and after finding his way into the area, the midfielder was denied by a low save from Albinson.
Southport’s only chance during the early part saw Devarn Green shoot wide after Jack Sampson’s initial effort from a Brad Bauress corner was blocked.
It was somewhat against the run of play that the Port opened the scoring on 21 minutes, Astles sliding a shot home after goalkeeper Russ Griffiths had denied Zehn Mohammed.
But the lead did not last for long, Chester equalising as George Waring converted from inside the area after a cross from the left by Akwasi Asante.
Southport qent close just before half-time, Sampson sending a shot wide after connecting with a half-volley from outside the area.
Yet Chester remained the stronger team and they took the lead four minutes after half-time, Asante making the most of a defensive mix-up before sending the ball past Albinson.
The visitors continued to press, Jackson having a shot deflected wide before Asante turned and lifted the ball over.
And Chester reinforced their superiority when Gary Roberts scored a spectacular third with a long-range rocket from 25 yards.
Southport: Albinson, Moahmmed, Doyle, Winnard, Astles, Morgan, Benjamin, Wood (Woods 84), Green (Oliver 74), Sampson, Bauress (Correia 57).
Subs not used: Hanford, Homson-Smith.
Chester: Griffiths, Morgan, Taylor, G. Roberts, Livesey, Grand, Jackson (Dudley 84), Gendon, Asante (K. Roberts 84), Waring, Stopforth.
Subs not used: Ngwatala, Elliott, Hughes.
Subs not used: 1,830
Referee: Dale Baines