Lambert quickly cancelled out the seventh-minute lead given to Forest by Matt Derbyshire before putting Nigel Adkins' side ahead and completing his treble by scoring a late winner after Radoslaw Majewski had equalised for the visitors three minutes before the break.
Saints had beaten the East Midlands side just once in the last 19 years, losing eight of the previous 12 meetings between the two clubs.
That solitary victory came in the Premier League in April 1997 when two late goals from Micky Evans saw Southampton triumph 3-1 at the City Ground.
This afternoon Dutch defender Jos Hooiveld made his Southampton debut after completing his loan switch from Celtic.
French midfielder Guy Moussi went straight into the Forest team to make his first appearance of the season after recovering from a calf injury.
Derbyshire linked up well with Ishmael Miller to open the scoring, converting his strike partner's low cross from close range.
However, the lead was shortlived as Lambert beat Lee Camp from 10 yards out to bring Saints level within 60 seconds.
Lambert fired a free-kick just over the bar after David Connolly was fouled by Wes Morgan.
Lambert continued to look dangerous and put the hosts ahead after 24 minutes when he nodded home Connolly's cross from the right.
Forest had a penalty appeal ignored by referee Iain Williamson when Miller went down under a challenge from Danny Fox before Derbyshire might have done better than head wide from Chris Gunter's cross.
Steve McClaren's men were rewarded for their endeavour in the 42nd minute when Miller and Derbyshire combined again, with the latter pulling the ball back for Majewski to beat Kelvin Davis with a low shot.
Only a superb save from Camp prevented Southampton from regaining the lead at the start of the second half. The Northern Ireland international tipped a well-struck shot from Adam Lallana round the post.
Lallana had another goalbound effort blocked by Morgan on the hour before Jose Fonte headed over the bar.
Camp produced another fine fingertip save to keep out a driven shot from Morgan Schneiderlin from the edge of the area after 67 minutes.
But Saints' pressure paid off eight minutes from time when Lambert headed home Fox's free-kick at the far post. Camp got a hand to the ball but could only push it into the roof of the net and Lambert wheeled off in celebration of his seventh goal of the season.
