Joe Kinnear's men had to come from a goal behind to take all three points after Danny Williams fired the home side in front after 50 minutes.
The visitors turned the game on it's head with three goals in an amazing five minutes.
Matthew Taylor drew the side's level in the 53rd minute and Matthew Spring (pictured) fired The Hatters in front just two minutes later.
Steve Howard hit a third for Luton to put them in firm control after 58 minutes and Spring netted his second in the 70th minute to wrap up the victory.
Shrewsbury moved into fourth spot in the table with a hard-fought 1-0 win over Oxford at Gay Meadow.
Darren Moss hit the only goal of the game after 29 minutes to give the home side all three points.
Click on fixture for full match summary
Kidderminster 1-4 Luton
Shrewsbury 1-0 Oxford
