Gurpreet Singh scored the all-important gaol in the 38th minute in the Group B tie of the North Zone qualifying round at the Ambedkar Stadium.
Punjab now have six points from two matches while Jammu and Kashmir remained on three from that many matches.
Jammu & Kashmir had two good chances to equalise in the second half but centre forward Prem Kumar and substitute Toufeeq Ahmed missed the target.
Dubey prodded from close after being set up by midfielder Rustam Pal.
Uttar Pradesh now have three points from two matches while Himachal are yet to open their account.