The top three teams win an automatic Champions League group-stage spot with the fourth going into the competition's qualifying rounds.
Bayern Munich secured their fifth successive league title on Saturday after crushing VfL Wolfsburg 6-0 to leave them 10 points clear with three games left as RB Leipzig, in second place on 63, drew 0-0 against Ingolstadt.
Nadiem Amiri hit the post for Hoffenheim early in the game and the hosts kept up the pressure throughout but could not score until Huebner rose high to drill in his header from a corner.
The win sent Hoffenheim into third, one point ahead of Borussia Dortmund, who drew 0-0 against Cologne on Saturday. Hoffenheim and Dortmund meet next week.
Veteran Halil Altintop scored twice as Augsburg crushed Hamburg SV 4-0 in their relegation derby to climb out of the drop zone.
The 34-year-old former Turkey international scored twice in the first half as Augsburg rose to the big occasion, leaving Hamburg boxed in their own half, unable to create any meaningful scoring chance in their own fight to stay up.
Read the full article on eurosport.co.uk: Huebner late goal sends Hoffenheim into Bundesliga top three