India looked to be coasting to victory with New Zealand in deep trouble at 131-6 while chasing 350 after opener Gill made just the 10th double hundred in ODI history.
Virat Kohli smashed a brilliant attacking century to set up a convincing 67-run win for India in the opening one-day international against Sri Lanka on Tuesday.
New Zealand's spinners strangled Pakistan on a turning wicket to win the second ODI by 79 runs Wednesday and level the three-match series 1-1.
Phillips counterattacked after a collapse and carried New Zealand over the line with 11 balls to spare. They rounded off their tour with a 2-1 victory, their first ODI series win on the subcontinent in 15 years.
Opener Ishan Kishan hit the fastest-ever double century in one-day internationals in just 126 balls to set up a 227-run consolation win for India in the third match against Bangladesh on Saturday.
Chasing 187 for victory, the hosts fell to 136-9 before Mehidy and Mustafizur Rahman put together a 51 run partnership — Bangladesh's best ever for the final wicket — to achieve their target with 24 balls to spare in Dhaka.
India skipper Rohit Sharma batted at number nine with an injured thumb and hit an unbeaten 51 off 28 balls to give Bangladesh a scare as India ended on 266-9 in 50 overs.
"It has been a fantastic ride with some incredible memories,” said Finch, who played 145 ODI matches, 54 as captain. "I have been extremely fortunate to be a part of some brilliant one-day sides.
Dhawan's innings off 99 balls with three sixes and ten fours earned him the "Man of the Match" award although the left-handed opener was not too pleased with his team's effort in the field.