Hit by a 10-point deduction at the start of the season for being in administration, Saints now have two points on the board after 11 games and are within sight of Wycombe Wanderers at the basement.
Rickie Lambert's explosive 13th minute volley gave Southampton the perfect lift, but midway through the half Gillingham teenager Luke Rooney equalised with a goal out of the blue.
Southampton hit the upright and squandered several good chances before scoring twice in a crucial 10-minute period before the break.
Papa Waigo restored Saints' lead after Lambert flicked on a throw-in on the right.
Lallana scored twice either side of half-time to seal Southampton's victory as, a minute before the break, he stylishly finished off a flowing move created by Jacob Mellis to make it 3-1. With 14 minutes left, Mellis was the creator once again, with Lallana bagging his second and Saints' fourth goal.