Carlisle continued their push for an automatic promotion place with a 13th consecutive home win.
Danny Livesey volleyed home Marc Bridge-Wilkinson's corner from 13 yards to open the scoring for Carlisle.
They doubled their lead when Peter Murphy out-jumped Luton goalkeeper Dean Brill to nod Chris Lumsdon's cross into an empty net.
The visitors pressed after half-time and David Bell reduced the deficit with a fine left-foot strike from 25 yards.
Carlisle: Westwood, Raven, Livesey, Murphy, Horwood, Taylor (Carlton 79), Bridge-Wilkinson, Lumsdon, Grant Smith (Jeff Smith 74), Hackney, Graham, Jeff Smith (Madine 90).
Subs Not Used: Howarth, Arnison.
Bookmark with:
What are these?