The target of 182 looked so easy for Delhi after Salt slammed 87 off 45 balls, hitting eight fours and six sixes.
An apt support to Salt by Rilee Rossouw (unbeaten 35 off 22 balls) took Delhi (187/3) home in just 16.4 overs.
Earlier, Bangalore boasted on Virat Kohli's 55 off 46 balls and Mahipal Lomror's aggressive unbeaten 54 off 29 balls to score 181/4 in 20 overs.
Mitchell Marsh was the best bowler for the hosts with a figure reading 2/21 in 3 overs.