Being one of few games to survive the fuel 'crisis', Kempston headed down the A6 to face regular opponents Barton Rovers.
Scott Dash made just two changes to Saturday's defeat to Newcastle Town, Dan Naylor coming in for Jack Quigley and Taylor Bakogeorge replacing Adam Drakulic.
In torrential rain, the hosts had the wind and the slope to their advantage, and gained a deserved lead just over half way through the half. A low cross from the right hand side found its way to the back post where the Barton striker was positioned to fire home from 6 yards.
Kempston were competing well, but gave themselves a mountain to climb just five minutes before the break. The left winger for Barton robbed possession and found his way into the box to square for the Barton midfielder.
The Walnuts made a half time change, Tre Charles replacing Saturday's goalscorer Marley Hamilton. Charles was involved early on in the half, and won himself a penalty after an excellent run into the box.
The winger got himself up and tucked away the penalty to get Kempston back into the game.
Half chances came and went for both teams, but no one could find the back of the net. Miguel Lopes DeMatos was shown a straight red late on after a deliberate clip on the Barton striker whilst through on goal.
Kempston are now placed 13th, and have to wait until the 16th October for their next league match, which will be against Harlow at Hillgrounds.