Siam Hangal scored the other goal for the home side while Clifford Miranda pulled one back for Dempo at the Bangalore Football Stadium.
Bengaluru FC maintained their unbeaten record at home as they went to the top of the table with 13 points from five matches.
On the other hand, the Goan side are struck on six points from as many matches.
Bengaluru's Manipuri striker Hangal -- adjudged the Man- of-the-Match -- opened the scoring for the hosts in the sixth minute with a superb volley from outside the box that beat a diving Dempo goalkeeper Subhashish Roy Chowdhury all ends up.
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Rooney scored his second goal of the match in the 61st minute to take his tournament tally to five goals when he made a run through the centre after receiving the ball from Darren Caldeira. With only the goalkeeper to beat, Rooney made no mistake as he slid the ball past Subhashish to make it 3-0 for the home side.
After getting one goal back, the visitors piled on the pressure in the Bengaluru half but some brilliant defending by John Johnson and Curtis Osano ensured that the home side end the match with a morale-boosting win.