New Zealand beat Bangladesh by 65 runs in a rain-shortened third Twenty20 International in Auckland on Friday to claim a series clean sweep.

With their innings reduced to 10 overs due to bad weather, Bangladesh were all out for 76 with three balls to spare, well short of the 142 target set by New Zealand.

The Black Caps made 141 for four after losing the toss and being asked to bat, with Finn Allen hitting 71 from 29 balls.

Spinner Todd Astle was the standout bowler, taking four wickets for 13 runs in his two over spell.

Captain Tim Southee said it was satisfying for the New Zealanders to notch their seventh home series win of the season on all formats.

"It's been a great summer and we've played some good cricket and seen a lot of guys come into the environment and do well," he said.

Bangladesh captain Liton Das said mistakes cost his side, including a series of dropped catches that allowed Allen to run away with the match.

"We're not playing good cricket in batting and fielding," he said. 

"We've been very good bowling but that's cost us. We're a young team and we're learning."

New Zealand made a blistering start, with Martin Guptill smashing three sixes in the first two overs.

Allen was also finding the boundary but rode his luck with two dropped catches as the Black Caps raced to 69 without loss after five overs. 

Guptill smashed 16 off the first three balls from Mahedi Hasan but the spinner had his revenge when the batsman was caught on 44 trying to clear the rope.

Allen brought up his maiden half century off 18 balls and was gifted another life when Soumya Sarkar dropped a straightforward chance. 

He finally fell in the final over, scooping a Taskin Ahmed delivery over his head to the fielder, but by then the damage had been done.

Bangladesh made a disastrous start, losing two wickets to paceman Southee in the opening over. 

They were starting to rebuild when Astle also claimed a brace, leaving Bangladesh teetering on 37 for four.

Astle's second over proved just as destructive and the tourists had no answer as the run rate climbed to an insurmountable level.