Garner bagged a sensational 35-yard strike 15 minutes from time to add to big defender Wes Morgan's first-half header and guide struggling Forest to only their second away win of the season.
Former Carlisle star Garner spotted that Southampton goalkeeper Kelvin Davis had strayed off his line before planting a superb chipped shot into the top right-hand corner to the delight of the 2,000 travelling supporters.
Morgan had earlier opened the scoring with his first goal of the season three minutes before the break.
Southampton's hapless defence left Morgan completely unmarked to nod home from Chris Cohen's pinpoint corner.
The defeat is a crushing blow for Southampton and their rookie manager Jan Poortvliet, whose side are now just a solitary point above third bottom Forest.
It could all have been different had midfielder Andrew Surman found the back of the net with a 20-yard thunderbolt after just 19 minutes, which crashed against Forest's left-hand post.
It was Saints, without a home win since September, who made the better start but they allowed Forest to take control when their all too familiar defensive lapses returned.
Home keeper Davis produced a brilliant finger-tip save to deny Arron Davies in the 16th minute after defender Alex Pearce had been left on his backside by Wales striker Robert Earnshaw.
Veteran midfielder Jason Euell also cleared off the line from visiting midfielder Matt Thornhill after Davis had flapped at Cohen's 27th minute corner.
Forest almost made the points safe in the 50th minute when Cohen headed inches over from Davies' free-kick.
Substitute Bradley Wright-Phillips threatened to spark a fightback by the home side when he flashed a right-foot shot inches wide with his first touch after coming off the bench but it was Forest who returned to the east Midlands with three vital points.