Saints dominated from the off against a lacklustre Yeovil side, who are still without a win away from home under manager Terry Skiverton.
Lambert was at the heart of all Southampton's best work and he opened the scoring inside 20 minutes, coolly dispatching a penalty after Marek Saganowski was felled in the area by Terrell Forbes.
Saints continued to press but the longer a second goal took to arrive, the more nervy the home players became.
But nerves were finally settled and the result secured five minutes into the second half when Saints were on the receiving end of a seemingly fortuitous penalty.
A long ball pumped into the Yeovil area appeared to brush defender Nathan Jones' arms but despite no appeals from the Saints players, the penalty was awarded and confidently smashed past stand-in goalkeeper Richard Martin to give Southampton a richly deserved first win to edge them closer to zero points.