Joshimar D'Silva pulled one back for the visitors in the second session.
With this win, Bengaluru FC move to 11 points from four matches to stay on top of the Points tally while the Kolkata outfit are yet to open their account after three matches.
John Johnson made the difference between the two teams. Apart from standing tall in the defence, Johnson opened the scoring for the hosts in the 12th minute as he headed it in following a corner from Beikhokhei Beingaichho. This was Johnson's third successive goal in as many matches and it bagged him his third successive Man of the Match Award.
The hosts could have scored another goal before the interval Malemnganba Meitei missed a great opportunity from close range.
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Despite trailing by two goals, it was the visitors who got off to a promising start in the second half. Mohammedan's Tolgay Ozbey made a couple of good moves in the first 10 minutes of the session but failed to put the ball past the Bengaluru goalkeeper Pawan Kumar. In the 77th minute, Pawan made a great save as to deflect Tolgay's right footer from inside the box.
The hosts also had their chances in the second half but were unlucky not to increase the margin. In the 69th minute Mohammedan Sporting Goalkeeper Sukhwinder Singh made a brilliant save to deny Rooney his second goal; and then, in the 84th minute, Robin Singh's left footer just went over the bar.