Erik Partaalu struck twice (24th and 45th minutes) while Lenny Rodriguez (57th) and Miku (87th) scored a goal each.
Kalu Uche scored from the dreaded spot in the 86th minute to pull one back for the Dynamos.
With this win, Bengaluru climbed to the top of the league table with six points from two matches.
Partaalu nodded home for his first goal after he received the header from Harmanjot Khabra on Edu Garcia's free-kick on the right. He scored his second goal as he headed the ball past Albino Gomes on Edu Garcia's corner-kick.
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Before Lenny could score the goal, Sunil Chhetri did well to find Udanta, who controlled the ball before sending in the cross on the left.
Nicolas Ladislao Fedor Flores (Miku) got the fourth goal for the home side in 87th minute as he released the shot that whizzed past Albino's reach.
The Dynamos were awarded a penalty -- from which Uche scored -- after John Johnson got his arms on the way while trying to clear Seitysen Singh's ball inside the box.
Bengaluru wasted yet another chance in the 77th minute after Albino did well to dive to his left and punched the shot taken by Miku after Delhi lost possession of the ball.
Both the coaches fielded the same teams which had beaten their respective rivals in their last encounters.
Dynamos had only one real chance in the match as Kalu Uche's header whizzed off-target off a Guyon Luis Fenandez cross inside Bengaluru's box in the 37th minute. Before having a go at the home side goal, Uche received a pass from Claudio Matias Mirajbe Correa.