The Hatters moved up two places in the Championship table after managing to frustrate the Potters' endeavours which leaves the play-off chasing club with only one win in their last eight league outings.
Potters boss Tony Pulis was able to call on the services of influential midfield trio Darel Russell, Salif Diao and Lee Hendrie again following last week's suspensions- and they should have given him an early lead.
Russell nodded inches over after getting on the end of a speared centre from Andy Griffin before Hendrie arrowed a pin-point pass in front of the marauding Mamady Sidibe.
The towering frontman sent his header wide before completing a trio of misses inside the opening half-an-hour- a tame shot and another lack-lustre header completing the hat-trick.
Then came eight minutes of folly which sparked the game into life after a pretty uninspiring 30 minutes of action.
It seemed a red mist had suddenly descended on the Britannia Stadium as both teams were forced to trudge into the half-time interval a man light.
A 30th minute bust-up between Sol Davis and Ricardo Fuller saw the City man push the Town defender - a petulant act which earned the Jamaican his second dismissal of the season.
But seemingly dissatisfied with his side's solitary numerical advantage the Hatters full-back tried to reduce the City ranks further with a wild lunge on Sidibe.
Referee Trevor Kettle greeted Davis' needless missile-launched assault with an instant red card - sparking a 15-man rumble around the dismissed defender.
Sidibe's woeful afternoon continued into the second-half until he was eventually stretched off on the 58th minute.
The Mali striker suffered a painful collision with the post after catapulting into a header which was saved at point-blank-range by Marlon Beresford.
Luton began to bare their teeth in the early second-half exchanges and came close to snatching a spectacular lead when Dean Morgan cut inside.
The jinking flank-man switched onto his left peg before smashing a rocket inches over the Potters goal and into the travelling Luton contingent.
But the Hatters' dominance was short-lived and they were back on the back-foot when Hendrie eyed up a well-placed free-kick.
The on-loan midfielder hooked a wicked effort over the Town wall only for Hatters skipper Steve Robinson to glance over from his own goal-line as the match finished in a disappointing stalemate.