Nigel Adkin's men did go one-up just before the quarter-hour mark when Guly Do Prado tried to pick out Lambert, but the ball didn't reach the striker as Hull defender Jack Hobbs turned into his own net.
The visitors could have made it two minutes later but Lallana shot wide after rounding Mannone.
Southampton turned the screw after the break and were two ahead after 59 minutes when centre-back Jos Hooiveld slid in to convert a Jose Fonte cross.
The Saints comfortably saw out the remaining half an hour and complete their 22nd win of the season.
Three points for Southampton move them five points clear at the top after Reading's loss at Peterborough and West Ham's 1-1 draw against Middlesbrough while defeat for Hull sees them fall from seventh to ninth.