Three first-half goals gave Eastbourne hope of escaping relegation and kept Southport firmly in trouble.
Matt Smart put Boro ahead with a free-kick from 40 yards before Richard Pacquette doubled the lead with a crisp strike from 12 yards.
It was 3-0 before the break when Pacquette's cross was turned into his own net by Karl Ledsham.
Steve Daly scored a late consolation from close range for Southport but it was Eastbourne's day.
Boro are now nine points from safety with six games left.
The win was especially sweet for defender Darren Baker, who made his 900th appearance for Eastbourne.
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Southport: McMillan, Williams (Barratt 46), Davis, Marsh-Evans, McGinn, Turner, Moogan, Ledsham, Kissock, McNeil (Daly 46), Whalley (Tony Gray 61). Subs Not Used: Dickinson, Blakeman.
Booked: Kissock.
Goals: Daly 90.
Eastbourne Borough: Banks, Baker, Austin, Jenkins, Taylor, Hutchinson, Purcell (Demetriou 52), Smart (Johnson 67), Matt Crabb, Kelly, Pacquette (Brinkhurst 80). Subs Not Used: Weatherstone, Holland.
Booked: Smart, Banks, Pacquette.
Goals: Smart 17, Pacquette 27, Ledsham 43 og.
Att: 923
Ref: S Smith (Yorkshire).
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