After skipper Mithun Manhas' 150 yesterday, the visiting side rode on Parveez Rasool's 120-ball 75 and Ram Dayal's 48 to get over the 400-run mark and grab the edge.
For Hyderabad, Anwar Ahmed was the best bowler with a haul of 5/92.
In reply, Hyderabad were 113/2 in 41 overs with opener Tanmay Aggarwal's 57 being their best individual score so far. Rohit Sharma picked up both the wickets that fell today ending the day with figures of 2/33.
Jammu and Kashmir 1st Innings: 460 all out in 131.2 overs (Mithun Manhas 150, Parveez Rasool 75, Anwar Ahmed 5/92).
Hyderabad 1st Innings: 113/2 in 41 overs (Tanmay Aggarwal 57, Rohit Sharma 2/33).