The hosts now face Pakistan on Friday, also in Christchurch, in the final of a series which is a tune-up for this month’s T20 World Cup in Australia.
Fresh from dispatching Pakistan by nine wickets on Tuesday, New Zealand put in another strong batting display to set Bangladesh an imposing 209-run target.
Despite a battling 70 from captain Shakib Al Hasan, Bangladesh fell short as they closed on 160-7.
New Zealand opener Conway smacked 64 off 40 balls and his partnership of 45 with Finn Allen, who departed for 32 after a superb Yasir Ali catch, set the tone.
The South African-born Phillips blasted 60 runs off 24 balls, including five sixes, to propel New Zealand to 208-5 in their 20 overs.
“The way Devon batted again was absolutely phenomenal, but it just happened to be my day with the bat,” Phillips said after being named man-of-the-match.
Adam Milne, back from an abdominal strain, struck in the fourth over of the Bangladesh chase when he bowled Najmul Hossain Shanto for 11.
Opening partner Liton Das soon followed, caught by Martin Guptill off the bowling of Michael Bracewell to leave Bangladesh on 47-2.
Captain Shakib offered the most resistance but once he was out, edging Tim Southee to wicketkeeper Conway, the game slipped away from Bangladesh.
“When you score a few runs, you feel better, but I thought we played quite well,” said Shakib.
“New Zealand put on a very good total and we were always behind in the game, but I thought we should have scored maybe 15 or 20 more runs, “We kept on losing wickets which cost us the game.”
A third straight defeat means Bangladesh cannot reach the tri-series final and their match against Pakistan on Thursday is a dead rubber.
New Zealand had rested captain Kane Williamson as they comfortably backed up Sunday’s eight-wicket win over Bangladesh to underline their T20 World Cup credentials.