Niklas Suele and Kramaric, with his 10th goal this term, struck late on after Hertha's Maximilian Mittelstaedt was sent off just before the hour. A Kramaric penalty had cancelled out Peter Pekarik's strike for the hosts in the first half.
The result lifted Hoffenheim to 48 points from 26 matches, two above Borussia Dortmund who visit Schalke 04 on Saturday, while Hertha's second home loss this season hit their quest for a top-four finish as they stayed fifth, six points off Dortmund.
Bayern Munich are 13 points clear at the top of the table before they host Augsburg on Saturday when second-placed RB Leipzig welcome bottom side Darmstadt 98.
The top three qualify for the Champions League group stage with the fourth-placed team entering the qualifying rounds.
Hoffenheim had keeper Oliver Baumann to thank in the 17th minute when he denied Salomon Kalou and cleared the rebound off the line.
Read the full article on eurosport.co.uk: Kramaric scores twice as Hoffenheim beat 10-man Hertha