After a goalless first half, the U’s went ahead through Adam Cunnington’s penalty before they were pegged back when Tobi Sho-Silva scored.
Delano Sam-York grabbed a winner on 75 minutes though to ensure United closed the gap on Hatters.
Third placed Alfreton moved to 13 points adrift after they eased past struggling Tamworth 4-2.
Town are back in action this weekend when they host Chester, while Cambridge play their FA Trophy final against Gosport Borough and Alfreton visit Halifax on Monday night.
For all the latest Luton Town FC news, reports, stats, player profiles, live match updates, MOM poll, prediction table and a complete fixture list, visit our Hatters Microsite.