Bengal had to sweat it out throughout the proceedings even though Nilkanta Paria put the team into lead in the 32nd minute in the East Zone leg tournament match.
Paria received an accurate cross from left flank on a counter-attack and found the target, leaving the home team defenders unmoved.
Jharkhand regrouped immediately and went all out for an equalizer but in vain as Bengal defenders successfully foiled all the moves.
Amid intensified attacking game, Konsham wanted to hold on a pass in the box but the ball deflected from his body and crossed the goal-line in the 69th minutes.
Also Read
Both teams committed fouls, forcing the referee to cautioned as many as seven players, including four of the host team.
Playing before the moderate home crowd, Jharkhand players kept building pressure in the last quarter of the proceedings.
Bengal, who had defeated Bihar, topped the point chart with six points with this victory and qualified for the final round from Group A.
In the crucial last league engagement of Group B, Railways, who had six points from two wins, will lock horns with Odisha, which had four points from one draw and a win, for a berth in the final found to be held in Goa from February 20 to March 10.