Andhra, trailing J and K by 79 runs in the first innings, shot out their rivals for a meagre 111 on the fourth and final day of the game and then reached the target for the loss of six wickets in 49.3 overs.
Andhra had to make 191 in 52 overs and they completed the chase when Siva Kumar struck J and K off spinner Parvez Rasool for a boundary.
Andhra were 82 for 3 at tea, needing 109 runs for victory, and were pushed back by a two-wicket burst in successive overs by medium pacer Ram Dayal to leave them at 149 for five.
Dayal sent back top scorer D B Ravi Teja (50) after breaking the stubborn fourth-wicket partnership of 62 between the two-down batsman and A G Pradeep (27) by castling the latter.
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But Hebbar kept his cool and although Rasool, who picked up the first three wickets, struck by dismissing M Sriram when Andhra were 174, he stuck to his task admirably and took his team past the finish line in the company of Siva Kumar.
Earlier, left-arm spinner Bhargav Bhatt ran through the J and K line-up by grabbing five for 60. He was given good support by medium pacer P Vijay Kumar, who claimed three wickets.
J and K, overnight 31 for 2, were all out in 55 overs after having made 334 in the first innings to which Andhra had replied with 255.
Andhra secured six points for the win to take their points tally to 8 from three matches while J and K remained on 7 points from three games.