David Mooney, Lloyd James and Dean Cox also got in the act for the League One leaders while Luke George and Matty Flynn registered for the visitors.
A dramatic opening 15 minutes left the home side with a two-goal lead and their opponents with two enforced substitutions.
Batt netted the opener after just three minutes and it was soon two-nil as Mooney netted his 12th goal of the season.
The Sandgrounders' problems mounted when goalkeeper Danny Hurst and Matthew Brown were injured in a collision and were both substituted.
But the visitors were given a boost when George touched the ball home from close range after a Jamie Milligan effort had been missed by debutant O's 'keeper Jake Larkins and rebounded off a post.
By half-time both teams had been forced into another substitution and on the stroke of half-time Orient replacement James sublimely turned a cross past David Stevenson to record his first goal for the club.
Batt added his second when netting from point-blank range after 56 minutes before being substituted on the hour.
Replacement Cox soon made a telling impression as he rifled home from 25 yards before Flynn reduced the deficit for Southport with a consolation goal late on.