Mills, who was left stranded on 27 from 25 balls, said the Black Caps got off to a poor start on a challenging pitch.
"It was the same wicket as the other day (first ODI on Tuesday night)," Mills said. "In the first innings it was definitely a wee bit tacky and the ball carried through nicely. But after 200 odd overs on the wicket naturally it gets a bit slower and that's where the spinners came into play.
''Bangladesh are a very good cricketing side in their conditions, a tough team to beat. They know their onditions well. The pitch conditions are a lot different to back home.
''It was obviously disappointing. We couldn't really get going with the bat and get a partnership going. The next game (on Sunday night) is a big game for us and we want to end the series on a high. We'll be up for the game, no doubt.''
After their famous 4-0 win against New Zealand at home in 2010, another clean sweep now beckons for Bangladesh who head into Sunday's final fixture full of confidence.
Taylor was dismissed by Gazi after attempting to hit his second straight six, only to be caught by Mahmudullah at long-on. Taylor struck two fours and a six on his 82-ball knock.
Taylor and Anderson put together 61 runs on the fourth wicket stand to keep New Zealand competitive after they were reduced to 3-45.
But Mashrafe removed Anderson by feeding him a wide delivery, which he edged to wicket-keeper Mushfiqur Rahim to be out on 37.
As Taylor and Brendan McCullum seemed to bail the side out of danger, Mushfiqur employed Mominul. His trick paid off with the part-time spinner trapping McCullum lbw on 14 to oust the biggest obstacle to Bangladesh's victory.
Mashrafe earlier made a good start for Bangladesh by taking Hamish Rutherford (1) with an inswinger delivery while Gazi and Razzak dismissed Anton Devcich (19) and Grant Elliott (14), respectively, to leave New Zealand on 3-45.
Earlier, New Zealand allrounders Anderson and James Neesham claimed four wickets each to dismiss Bangladesh on 247 with one over to spare.
For Bangladesh, opener Tamim Iqbal top-scored with 58 off 86 balls that included five boundaries and one six, while Rahim and Mominul collected 31 runs each.
Gazi was the other notable scorer with 26.
Anderson returned 4-40 while Neesham took 4-53 after Bangladesh won the toss and decided to bat first at Sher-e-Bangla National Stadium.
Tamim and debutant Shamsur Rahman gave Bangladesh a solid start by adding 63 runs for the opening stand, in which the latter made 25.
Later, Bangladesh failed to build up any significant partnership as the Kiwi bowlers bounced back strongly to take the wickets at regular intervals.
The big blow came for Bangladesh when Anderson got in-form Mominul Haque with a slower to take him out on 31. Mominul struck five boundaries on his 34-ball knock.
Tamim, after scoring his 25th half-century, played a poor shot to be bowled out by Anderson. However, he went past Shakib Al Hasan to be the highest run-getter for Bangladesh with his total on Thursday.
Neesham had taken Rahim to shatter Bangladesh's hope of amassing any big total.
Anderson and Neesham varied their pace to fool the Bangladeshi batsmen and reaped the benefit. With the two bowlers operating shrewdly in the mandatory power play between 36 overs and 40 overs, Bangladesh earned only 35 runs in three wickets.
Bangladesh won the rain-disrupted first match on Tuesday.
-nzherald.co.nz and AP
