Glenn Phillips scored an unbeaten 40 under pressure as New Zealand beat Bangladesh by four wickets in the second Test on Saturday to finish the two-match series level.

Set a chase of 137 in Dhaka, the visitors reached 139-6 an hour into the fourth day's final session with Phillips, who made 87 in the first innings, receiving able support from Mitchell Santner.

Santner capped in on a fine all-round performance with 35 not out after his 3-51 earlier with the ball.

New Zealand had an eight-run lead in the first innings with Phillips guiding the side to 180 from a precarious 46-5, in reply to Bangladesh's 172.

"That eight runs mattered a lot," player-of-the-match Phillips said.

"We pride ourselves on fighting for as long as possible. Our spinners bowled incredibly."

Mehedi Hasan Miraz claimed 3-52 and Taijul Islam chipped in with 2-58 before Phillips and Santner, who shared 70 in their unbroken seventh-wicket stand, denied Bangladesh their hopes of a first Test series win over the Black Caps.

"It was a bit of a scrape there, nice to come out on the right side of it," said New Zealand captain Tim Southee.

"The guys just trusted their game. On this pitch, you can still play your way," he added. "At times, Bangladesh showed it as well. It was a matter of time before one had your name on it."

Bangladesh struck early as Shoriful Islam removed Devon Conway for two before the spinners came into action.

Miraz dismissed Henry Nichols for three and Tom Latham for 26 between Taijul's wickets of Kane Williamson (11) and Tom Blundell (two).

Miraz's consistent bowling was rewarded when he forced an edge from Daryl Mitchell (19) at slip.

"The bowlers did a great job," Bangladesh skipper Najmul said.

"In the first match, we played really good cricket. This game we had our opportunities, but we couldn't take them."

Earlier, Ajaz Patel took 6-57 for his fourth five-wicket Test haul and Santner complemented with his left-arm spin to help New Zealand bowl out Bangladesh for 144 runs in the second innings.

Resuming on 38-2, Bangladesh began aggressively but managed just 106 runs in 27 overs during the fourth day's extended opening session.

Zakir Hasan was the only batsman to put up a fight, top-scoring with 59 before the Kiwi bowlers wrapped up the innings.

Patel brought Zakir's defiant innings to an end, forcing him to top edge at slip after Santner removed Nayeem Hasan for nine.

Fifteen wickets fell on the opening day before rain washed out the entire second day and the opening session of the third.

Bangladesh won the opening Test in Sylhet by 150 runs.