A first-half strike from Sam Bennett and a goal from Andrew Oluwabori just after the hour mark settled the contest in the hosts’ favour.
The Bucks created little in the heavy rain but did miss a huge chance to get back into the game following Kettering’s opener when Matty Carson’s penalty hit the post.
The first chance of the game fell to the hosts when a cross in from the right found Bennett but he couldn’t keep his effort down.
Telford had the ball in the net after 17 minutes through Harry Flowers, but the effort was quickly ruled out by the referee due to a foul by Flowers.
The visitors pressed again with Devarn Green cutting inside before firing a shot from 25 yards that failed to trouble former Shrewsbury keeper Cameron Gregory.
It was the hosts who threatened next when Andrew Oluwabori produced some impressive hold-up play before sending Ben Sault through on goal, but he could only fire straight into the hands of Bucks keeper Luke Pilling.
But Pilling was beaten four minutes before half-time.
Bennett was the man on the mark, beating Jordan Piggot before firing past Pilling low and hard at the near post.
The last action of the half saw Robbie Evans fire an effort off target for Bucks.
Telford made a bright start to the second half with Green in the thick of things again as he cut inside and tried his luck with a curling effort that was deflected wide for a corner.
The Bucks then squandered a great chance to get back on level terms when they were awarded a penalty on 56 minutes.
Carl Baker was upended in the area but the resulting spot-kick from Carson struck the base of the post.
The action quickly swung to the other end of the pitch where Telford survived a real scare.
Flowers’ back pass was completely missed by Pilling but fortunately for the visitors the ball rolled just wide of the post.
Telford were not so fortunate just after the hour mark when some sloppy play was punished by Kettering.
The visitors gifted the ball to Oluwabori and he calmly slotted past Pilling to make it 2-0.
Telford boss Paul Carden reacted by making a double change that saw Sam McLintock and Josh Dugmore replace Prince Ekpolo and Evans.
Kettering then almost put the result beyond doubt when Luke Ward’s effort from the edge of the area beat Pilling but struck the post.
Oluwabori was continuing to prove a handful for the Bucks defence and he threatened to get in on goal only to be denied by a last-ditch challenge from Matty Brown.
Telford created an opening for McLintock but he could only find the palms of Gregory.