In bone-chilling conditions in the Indian capital, Bell (108) stole the show, captain Cook (44), Eoin Morgan (52) and Craig Kieswetter (41) made significant contributions to the total.
At one stage, it did not look like that England XI will get close to 300 from 130/3 in 28.3 overs. But Bell and Morgan turned the tide by sharing the fourth-wicket partnership of 113 runs off 91 balls.
Kieswetter came up with some lusty shots towards the end, hammering Delhi pacer Sumit Narwal for two sixes to finish the innings.
Bell and Cook ensured a solid start for the visitors before Narwal found the stumps of the skipper, making it 70/1 in 15.3 overs. It was a good knock for Cook ahead of the first ODI in Rajkot Friday as he had missed the Palam game due to cold.
Bell continued from where he left off in Sunday's tie when he scored 91. He was watchful initially but played all the shots in the book later on. In all, he hit 10 fours and two sixes.
Delhi speedster Parvinder Awana proved expensive, leaking 53 runs in 8 overs.
Varun Sood was the stand-out bowler for the domestic team, picking up three wickets, including Bell's.
A handful of spectators braved the cold to watch the game and reserved their loudest cheer for Kevin Pietersen, who was rested.
Delhi responded with a big start of 98 between Dhawan and youngster Unmukt Chand (37). Dhawan departed after a 109-ball knock in which he made 110 runs with 14 fours and three sixes.
His wicket left Delhi needing 107 runs from 93 balls, which Miling and Bhatia managed on their own.
Miling scored an unbeaten 78 off 85 balls with seven fours and three sixes while Bhatia took just 33 balls to score 45 with eight fours.
England’s series of five ODIs against India starts on January 11 in Rajkot.