Zaman played a knock for the ages on Sunday before being run out in the last over, breaking the record for the highest score in an ODI innings when batting second.
Highlights, New Zealand vs Bangladesh, 3rd T20I at Auckland, Full cricket score: Hosts complete series sweep with big win
Catch the live scorecard and updates from the third and final T20I between hosts New Zealand and Bangladesh on our blog.
The result means the Black Caps have won all seven of their home series this season, an unbroken run of success on New Zealand soil that extends to nine if results against India last year are included.
New Zealand went into the match without six frontline players including Kane Williamson and Trent Boult and stand-in captain Tim Southee said it was pleasing to see the new blood perform with the bat.
Uncapped Allen, 21, made it into the 13-man squad on the back of his outstanding domestic T20 form for Wellington, where he averaged 56.88 and topped the run-count with 512 in the Super Smash.
England are seven points ahead of India, who were third before the away series against Australia. Australia's 2-3 loss to New Zealand in a recent five-game series pushed the side below India with just one point separating the two.
Southee was found to have breached "Article 2.8 of the ICC Code of Conduct for Players and Player Support Personnel", a Level 1 breach.
New Zealand vs Pakistan: Kyle Jamieson claims five-for as Kiwis bundle out visitors for 297 on Day 1 of second Test
Kyle Jamieson took a five-wicket haul as New Zealand bowled out Pakistan for 297, anchored by a sterling 93 from Azhar Ali on Day 1 of the second Test against New Zealand in Christchurch.
New Zealand vs Pakistan: Tim Southee, Trent Boult leave visitors staring at defeat on Day 4 of first Test
New Zealand declared their second innings at 180 for five and Pakistan, set an unlikely target of 373, will go into the final day at 71 for three.
New Zealand vs Pakistan: Tim Southee enters elite 300-wicket club on Day 4 of first Test, third Kiwi to do so
Globally, 32-year-old Southee is only the 34th bowler to reach 300 wickets in the history of Test cricket.
New Zealand vs West Indies: Bowlers run riot as Black Caps clinch innings victory to seal series and top Test rankings
New Zealand also stayed in the hunt for the inaugural World Test Championship final as they overtook England to move into third in the standings behind Australia and India, who start a four-Test series this week.
New Zealand vs West Indies: Jason Holder's gritty unbeaten 60 keeps Windies alive on thrilling Day 3 of second Test
West Indies require a further 85 runs with four wickets remaining to make New Zealand bat again and avoid a second innings defeat.
New Zealand vs West Indies: Hosts' swing bowling display leave Windies struggling for survival on Day 3 of first Test
A relentless swing attack spearheaded by Tim Southee left the West Indies struggling for survival with only four wickets left and a 185-run deficit after the third day of the first Test against New Zealand in Hamilton.
Highlights, New Zealand vs West Indies, 1st T20I at Auckland, Full Cricket Score: Hosts win by 5 wickets
Follow live action from New Zealand vs West Indies 1st T20I at Auckland on our blog
Coronavirus Outbreak: Inaugural edition of Lanka Premier League postponed due to unavailability of players
The T20 League was scheduled to start on 28 August, subject to approval from the government and Ministry of health but the 14-day compulsory quarantine period turned out to be an issue with regards to foreign players.
Liam Plunkett, Tim Southee among 93 international cricketers listed for inaugural Lankan Premier League
The inaugural edition of the Lankan Premier League will take place between 28 August and 20 September, with the Dubai-based Innovative Production Group being awarded "total rights" of the LPL for five years.
Opener Tom Latham has won the Redpath Cup as New Zealand’s best batsman, breaking a seven-year streak in which the trophy was won by either Kane Williamson or Ross Taylor.
Tim Southee claims top honours in Players' Association awards, Sophia Devine wins Cap in women's category
New Zealand pace spearhead Tim Southee claimed the top honours in the annual Players' Association awards for his "compelling" performance in the home series against India, while Sophie Devine bagged the top women's award.
Chappell-Hadlee Trophy: New Zealand's pace bowling trio of Trent Boult, Matt Henry, Lockie Ferguson return for ODI series against Australia
New Zealand will take a full strength bowling attack to Australia for the one-day international series later this month after including Trent Boult, Matt Henry and Lockie Ferguson in their squad