The U's has not tasted victory since the 2-0 success over Port Vale on October 2, but they had the better of the scoring chances against the Hatters.
It was an extremely tight game where both sides tended to cancel each other out as Luton seemed just happy to extend their good run with just one defeat in their last 13 league fixtures.
Chances are few and far between until Colchester mounted several attacks late on.
Neil Danns looked on course to break the deadlock when he pounced onto Craig Fagan's flick only to see his shot well blocked by keeper Marlon Beresford.
Beresford was the busier of the two goalkeepers and he came to his side's rescue, again in the last minute of normal time palming away midfielder Kevin Watson's low effort inside the area.
Luton had very few scoring opportunities with the best of them falling to Steven Howard, but he blasted the shot over the top in the first half and was closer with a header that drifted wide in the second period.
Colchester's best opportunity in the first half fell to Joe Keith who had a shot from the edge of the box which was smothered by Beresford.
Colchester old boy Rowan Vine, who had scored both goals for Luton in the corresponding fixture at Kenilworth Road, which ended in a 2-2 draw, did not have much joy against his club this time round. He was well shadowed by defender Pat Baldwin and was eventually substituted.
Colchester remained stuck in the lower half of the table, just a few points clear of the relegation zone, and it is their poor home form that has kept them there.
However they have another chance to record a rare home victory when Walsall are the visitors on Tuesday evening.
For Luton however this was a point gained for a hard working performance.