The Saints started the first half brightly, threatening through Gaston Ramirez before going in front with just five minutes on the clock.
Ramirez's cross was nodded down by Jay Rodriguez for Schneiderlin to poke the ball past Brad Jones in the Liverpool goal and make it 1-0.
Southampton should have been 2-0 to the good in the 10th minute when Lambert found himself clean through on goal, only to direct his effort straight at Jones.
The hosts' dominance continued, with further chances falling to Ramirez and Rodriguez, but it took them until the 32nd minute to grab their second goal.
Martin Skrtel brought down Lambert in the danger zone, and the Saints striker took the resultant free kick himself, finding the back of the net with the help of a wicked deflection off Daniel Sturridge.
Liverpool pulled a goal back against the run of play right on the stroke of half time through Philippe Coutinho to give them a fighting chance in the second period.