Southampton made all the running in a goalless first period, Lambert testing Owls debutant keeper Richard O'Donnell with a low free-kick and Adam Lallana also going close with a low drive in the opening 20 minutes.
Saints captain Dean Hammond also forced a smart save from youngster O'Donnell with a 20-yard volley after the break, but the rookie keeper could do nothing about Southampton's opener.
From Alex Chamberlain's pinpoint corner, Fonte rose highest to thump home a powerful header from six yards and give the home side the lead on the hour.
The lead was doubled just five minutes later, Lee Barnard's deflected shot bouncing perfectly into the path of the onrushing Lambert, who half-volleyed home from 10 yards.
Nigel Adkins' side were now rampant, the impressive Lallana unlucky not to add a third after seeing a vicious first-time drive crash into the base of the post with the keeper beaten. Teenage sensation Chamberlain also went close with a curling effort which O'Donnell acrobatically palmed to safety as Southampton comfortably wrapped up a fourth consecutive league win.