Blue Square Bet Premier newcomers Alfreton were denied a first win of the season by a series of good saves from Southport keeper Tony McMillan.
Nathan Arnold twice failed to beat the Sandgrounders man, as did Jamie Mullan, before the break.
Dan Lowson in the Alfreton goal was equal to a close-range effort by Simon Grand in the 41st minute and subsequent attempts by Kevin Lee and Tony Gray.
McMillan was again on hand to keep out Theo Streete in injury time.
Alfreton Town: Lowson, Law, Young, Streete, Franklin, Moult (Hall 80), Brown, Matt Wilson, Mullan (Anthony Wilson 74), Clayton, Arnold.Subs Not Used: Senior, Jarman, Mackin.
Booked: Matt Wilson, Arnold, Streete.
Southport: McMillan, Smith, Akrigg, Grand, Lever, Lee, Ledsham, Benjamin, Kissock, Whalley, Gray (Daly 82).Subs Not Used: Nemes, Brown, Owens, Ordish.
Booked: Lee, Whalley.
Ref: Richard West (East Yorkshire).