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.
But Hertha's Slovak defender Pekarik did better for the hosts in the 32nd, firing home from 15 metres for his first league goal in his 151st Bundesliga appearance.
The visitors levelled with Kramaric's 39th minute spot kick following Mittelstaedt's handball and, with Hertha's first-half pace evaporating after the break, the hosts suffered another blow when Mittelstaedt was dismissed for a second booking.
Croatian Kramaric will be asking himself how he failed to score again in the 66th when he fired a thundering shot onto the crossbar and then volleyed the rebound against the post.
Two minutes later it was Hoffenheim midfielder Kerem Demirbay's turn to have a go before Suele scored with his 30-metre missile. Kramaric then tapped in the third goal in the 86th to complete a winning night for the visitors.
(Reporting by Karolos Grohmann; editing by Ken Ferris)
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