The Poppies were unable to recover after trailing 2-0 at half-time as the hosts scored two penalties.
Wilson Carvalho gave them hope with a spot-kick of his own after the break but they couldn’t find an equaliser.
Their hopes of qualifying for the top five are now slim with Hungerford Town and Weymouth both in action tomorrow night (Tuesday) before the Poppies return to action in their final home game of the season against Bideford on Thursday night.
The Poppies suffered an early setback when goalkeeper Craig Hill conceded a penalty, which was converted by Ashley Sammons.
However, Kettering had their chances with Rene Howe being inches wide from a Liam Bateman cross while David Popa headed over from another Bateman delivery.
But Redditch made it 2-0 before the break with a second spot-kick, again awarded for a foul by Hill on a forward and again scored by Sammons.
Kettering gave it a real go after the break though and they pulled a goal back with a penalty of their own on 68 minutes when Liam Canavan was brought down and Wilson Carvalho made no mistake from 12 yards.
Hill made a fine save to keep the Poppies in it at the other end but they continued to create opportunities with substitute Silvano Obeng being just off target while Ben Stephens had an effort blocked after a good move.
But they couldn’t find a way through and will now have to win their last two games and hope for some serious help from elsewhere if they are to squeeze into the play-offs.