Kumar scored both the goals for the bank team on either side of the breather of the match played at Bakshi Stadium.
The Kapurthala team, which was trailing after conceding the first goal in the 26th minute, tried hard to get an equaliser for rest of the match.
The visitors went broke in the last five minutes in the search of the equaliser but ended up conceeding another goal.
Chief Minister Omar Abdullah gave away the prizes to the champion and runner-up teams.
Police Martyr's football tournament was started in 1998 in memory of Inspector Mushtaq Ahmad who was killed in a militant attack in Lal Chowk area of the city a year earlier.
The tournament was later dedicated to the memory of all the police personnel who have laid down their lives fighting militancy in the state.