The 16-year-old scored with a stunning lob after 23 minutes to give the Saints their first win in five Championship games.
A long clearance upfield was not dealt with by Luton defender Kevin Foley and Walcott lifted a beautifully flighted left-footed shot from the byline over keeper Dean Brill.
Brill, a replacement for the crocked Marlon Beresford was perhaps at fault with his positioning but it was hard to argue with the finish.
Matt Oakley nearly doubled the lead 10 minutes later when his free-kick from a similar position to which Walcott scored from was parried away by Brill.
The home side then went close again five minutes later when Rory Delap's long throw was headed on by Kenwyne Jones, only for Neil McCann to flick the ball narrowly over.
Luton created little in the opening period but nearly grabbed an equaliser just before the interval.
Paul Underwood sent a free-kick into the penalty area, Antti Niemi flapped at the cross and Chris Coyne was unlucky to see his improvised overhead kick headed off the line by Delap.
Walcott, the best player on the park by far, raced clear of the Luton defence in the 56th minute but finished tamely, shooting straight at Brill with the goal at his mercy.
For all their possession, Southampton failed to kill Luton off and they were fortunate not to concede a late equaliser when Niemi again flapped at an Underwood cross and Danny Higginbotham was forced to clear off the line with Steven Howard ready to pounce.
The win, Dave Bassett's first as caretaker manager, was marred at the end by Delap's second yellow card for a rash, mis-timed challenge on substitute Rowan Vine.