Lambert struck twice in the first half before sealing his treble with a second-half penalty, taking his tally to 19 league goals, as Saints extended their unbeaten run to six games.
West Ham started the day as leaders but their stalemate with Crystal Palace provided Nigel Adkins' side with the opportunity to leapfrog them and they took full advantage.
Watford handed a debut to Manchester United loanee Tomasz Kuszczak in goal but he was culpable for the opening goal, finding himself stranded as Lambert nodded in.
The keeper could do nothing with the second goal shortly afterwards as Lambert fired home from the edge of the box.
Carl Dickinson gave the striker a chance to wrap up his hat-trick when he fouled Tadanari Lee in the box and Lambert duly obliged by blasting in the penalty.
The first chance of the game very nearly fell to Troy Deeney when Kelvin Davis' rushed clearance came straight to him but the striker was unable to control the ball.
It was an error from Davis' opposite number which led to the game's opening goal in the 13th minute.
Debutant Kuszczak had ample time to get to Jose Fonte's cross but he hesitated and was caught out of position, allowing Lambert to loop his header over the goalkeeper.
The visitors were buoyed by the opening goal and Lambert managed to double their lead just eight minutes after his opener.
Adrian Mariappa failed to clear the ball and Saints broke quickly through Morgan Schneiderlin and Adam Lallana.
The latter used trickery to create some space and laid the ball back for Lambert, who emphatically drilled the ball into the bottom corner at the first time of asking.
Lallana came off injured at the end of the first half but it did not slow Southampton's attacking juggernaut.
Japanese striker Lee should have put the result beyond doubt early in the second half but he scooped a great chance over the crossbar.
The Hornets had offered little in front of goal but they should have pulled one goal back when Mark Yeates' cross was nodded wide by John Eustace. The Watford skipper was stretching and should have let the delivery reach debutant Marcello Trotta, who was well placed.
Lee raced through 19 minutes from time only to be denied by a fine Kuszczak save, but Dickinson pushed the striker in the aftermath and referee Tony Bates awarded a penalty.
Lambert rifled the spot-kick into the top corner of the net and out of Kuszczak's reach to complete his hat-trick.