The Elland Road site were taken to extra-time against the Non-League outfit before they finally won the tie with four goals in eleven extra-time second half minutes and sealing a third-round FA Cup tie against Manchester United at Old Trafford.
Luciano Becchio headed the home team in front as Leeds dominated the first hour, with the scorer hitting the post and Lee Harper making several saves.
Former Leeds player Anthony Elding headed Kettering level after the break.
Leeds took control in the second half of extra-time, Tresor Kandol heading home between two strikes from Mike Grella before Jermaine Beckford struck.
The scoreline was harsh in the extreme on the non-league team.
There was little to choose between the two sides in the first half of extra-time but after the restart Leeds took control with four goals in 11 minutes to ensure the tie would not go to a penalty shoot-out.