A single judge bench of Biswanath Rath also suggested the aggrieved students to apply for re-evaluation of their answer sheets by 2 pm tomorrow and asked the CBSE to publish their results by June 10.
Earlier in the day, the students and their parents launched a hunger strike in front of the CBSE's regional office in Bhubaneswar.
"We welcome the high court judgement. The parents' association will move the court tomorrow seeking justice for all the students who have been victim of the CBSE's discrepancies," said Sudarsan Das, one of the parents who was on hunger strike.
The strike will continue till fulfillment of their demands, the agitators said.
Besides demanding a CBI probe into the alleged fiasco in publication of results, the agitators also demanded reevaluation of the answer scripts of those who had applied for rechecking of their answer sheets.
One of the girl students who was on hunger strike fainted at the venue due to dehydration. The police rescued the girl and rushed her to the Capital Hospital for treatment.
Yesterday, a male student had attempted self-immolation in front of the CBSE's regional office in Bhubaneswar. He was, however, rescued by police and parents.
Meanwhile, a delegation of NSUI met Odisha Governor S C Jamir and submitted a memorandum highlighting the alleged discrepancies in the CBSE's Class 12 results.
The governor assured to look into the matter, NSUI Odisha unit president Itish Pradhan said.