Responding to Bangladesh's first-innings total of 172, New Zealand scored 180, securing a slim lead of eight runs in the ongoing Dhaka Test on Friday.
The second day of the match was washed out due to day-long rain influenced by the cyclonic storm Michaung.
The third day's play was also delayed due to a wet outfield, resuming only after the first session.
New Zealand were at 55 for five at the end of day one. The match witnessed the fall of 15 wickets on day one, with spinners accounting for 13 of them.
On the third day, New Zealand added 125 runs with the remaining wickets. Phillips adopted an aggressive batting style, posting 87 off 72 balls with nine fours and four sixes.
For Bangladesh, Mehidy Hasan Miraz and Taijul Islam took three wickets each, while Shoriful Islam and Nayeem Hasan took two wickets each.
Earlier, Bangladesh posted 172, with Mushfiqur Rahim scoring the highest at 35. Mitchell Santner and Phillips took three wickets each for New Zealand.
Bangladesh won the first Test of the series in Sylhet by 150 runs and aims to seal the series in this match.