Southport held on for a draw despite playing most of the second half with 10 men after Michael Powell was sent off. Mark DeBolla gave Gravesend an early lead, curling home a 30-yard free-kick but Mark Boyd replied for Southport in identical fashion.
Fleet regained the lead five minutes later when Luke Moore fired in a low shot from 12 yards out.
But the hosts were level again before the break when Powell found the bottom left corner from the edge of the area.
Southport: Paul Harrison, Lane, Lee, Rowland, Hoolickin, Blakeman, Boyd, Powell, Olsen (Clancy 81), Booth (Baker 71), Martin (Gray 54).
Subs Not Used: Bagnall, Barry.
Sent Off: Powell (48).
Booked: Lee, Powell.
Goals: Boyd 32, Powell 44.
Gravesend: Cronin, James Smith, McCarthy, Ross Smith, Ricketts (Sodje 90), Slatter (Coleman 76), DeBolla, Quinn, Keeling, Moore, MacDonald.
Subs Not Used: McKenna, Roberts, Mott.
Booked: James Smith.
Goals: DeBolla 12, Moore 37.
Att: 861
Ref: R Wigglesworth (Lancashire).