Despite a spirited second-half showing, the Hatters spluttered to their second goalless draw in successive games and ultimately tasted failure in their bid to overturn their 30-point deduction with four games remaining.
The game saw Jack Lester threaten two minutes in as he just failed to get a touch on a Jamie Lowry ball from the right, before Keith Keane dragged a 20-yard shot wide for the Hatters four minutes later.
Lester then prodded at Dean Brill with a near-post effort from another Lowry cross in the 15th minute, before the same player went even closer three minutes later, chipping over Brill but also over the bar after Martin Gritton had flicked on a Jared Wilson long ball.
Luton finally settled and Keane hit a dipping half-volley just over from 25 yards after a clever Kevin Nicholls corner in the 22nd minute.
Three minutes later the hosts should have taken the lead when Lloyd Kerry collapsed with injury as he was chasing back allowing Claude Gnakpa a run on goal.
But with team-mate Tom Craddock in the clear beside him, Gnakpa inexplicably dawdled and was tackled to the frustration of the home faithful.
Kerry made way for Allan Goodall and the ex-Hatter almost had an immediate impact as he ended a 30-yard run with a curling 25-yard effort that Brill saved at the second attempt.
On the half-hour mark Goodall slipped in Gregor Robertson overlapping on the left, but the full-back spurned a great opportunity firing over from 15 yards.
More chances came for both sides before the break with Derek Niven heading a Lowry cross over from six yards in the 34th minute, Lester firing a 20-yard snapshot just off target a minute later and Craddock seeing a 12-yard strike deflect wide off Daniel Hall six minutes before the interval.
Brill also had to be alert to hold a curling 25-yard free-kick from Robertson as the Spireites continued to show their attacking threat.
Luton upped their game and three minutes into the second period a looping Sam Parkin header hit the top of the crossbar after Nicholls' cross.
The Hatters then twice went close to breaking the deadlock in the space of 60 seconds on the hour mark. First Parkin could only fire straight at Tommy Lee after being played in by Nicholls, then Lee did well to smother at the feet of Gnakpa as the Frenchman burst into the penalty area from the left flank.
Lee was again in impressive form as he dived full length to keep out - and hold - a low 22-yard effort from Asa Hall in the 66th minute.
In the 76th minute Parkin looked all set to score from substitute Ian Henderson's cross, only to put his header over from five yards.
Town kept plugging away and George Pilkington sent an 18-yard shot on the turn just wide after Ed Asafu-Adjaye's 83rd minute cross.