The striker opened the scoring in the fifth minute as he tapped in a Liam Nolan knock-down from a corner.
Nolan then got on the score-sheet himself to double the hosts' advantage in first-half stoppage time before Southport made it 3-0 shortly after the break when Allen got his second of the game.
Maidstone pulled a goal back as Yemi Odubade's close range finish reduced the deficit for the visitors.
The Stones made it 3-2 in stoppage time when Bobby-Joe Taylor dispatched a penalty but it proved to be too late for Maidstone.
Report supplied by the Press Association.
Match ends, Southport 3, Maidstone United 2.
Second Half ends, Southport 3, Maidstone United 2.
Goal!  Southport 3, Maidstone United 2. Bobby-Joe Taylor (Maidstone United).
Substitution, Maidstone United. Liam Enver-Marum replaces Seth Nana Ofori-Twumasi.
Substitution, Southport. Ashley Grimes replaces Jordan Lussey.
Substitution, Southport. John Cofie replaces Andrai Jones.
Callum Howe (Southport) is shown the yellow card.
Substitution, Maidstone United. Ben Greenhalgh replaces Bradley Hudson-Odoi.
Substitution, Southport. Liam Hynes replaces James Caton.
Jamie Coyle (Maidstone United) is shown the yellow card.
Goal!  Southport 3, Maidstone United 1. Yemi Odubade (Maidstone United).
Substitution, Maidstone United. Jack Evans replaces Dan Sweeney.
Goal!  Southport 3, Maidstone United 0. Jamie Allen (Southport).
Second Half begins Southport 2, Maidstone United 0.
First Half ends, Southport 2, Maidstone United 0.
Goal!  Southport 2, Maidstone United 0. Liam Nolan (Southport).
Seth Nana Ofori-Twumasi (Maidstone United) is shown the yellow card.
Goal!  Southport 1, Maidstone United 0. Jamie Allen (Southport).
First Half begins.
Lineups are announced and players are warming up.
Jamie Allen scored at the beginning of each half as Southport defeated Maidstone in the National League.