The League One outfit had chances to add further goals to Rickie Lambert's 36th-minute winner but found visiting keeper Kevin Pilkington in inspired form.
Pilkington - on-loan from Notts County - had to be at his best to keep out efforts from Adam Lallana, Michail Antonio and a long-range free-kick from Lambert.
And when the home side did finally find a way past the stopper they were frustrated by Luton's brave defending, Lambert seeing his header cleared off the line.
The striker was to be rewarded for his persistence, though. The £1million signing from Bristol Rovers bagging his 20th goal of the season with a superb 25-yard free-kick.
The Hatters launched a second-half fightback in search of an equaliser but former Luton keeper Kelvin Davis was on hand to deny Asa Hall and Claude Gnakpa.