In the third game of the five-match series, the Black Caps were put into bat and won by 45 runs after restricting Pakistan to 179 for seven and amassing an incredible 224 for seven.
It came after they had won the first two matches by scores of 46 and 21 runs, respectively.
The daring Allen blasted 16 sixes and five fours in his furious innings, building on his 74 off 21 balls in game two. He often hit the ball over the fence.
The opener’s 137, which beat Brendon McCullum’s previous best of 123, is the highest score by a New Zealander in a Twenty20 international. It also tied the world record of 16 sixes in an innings held by Hazratullah Zazai of Afghanistan.
He dominated the bowling, hitting three sixes, two fours, and a single to take 27 off of Haris Rauf’s over.
On a miserable day with the ball for Pakistan, Rauf gave up 60 runs in his four overs, while Mohammad Nawaz gave up 44 and Shaheen Afridi 43.
Tim Seifert and Allen put on 125 for the second wicket after Devon Conway was dismissed for seven early on. Seifert only made 31 as he chose to play singles in order to keep the hard-hitting opener on strike.
After Allen hit balls out of the ground three times, the umpires had to call for replacement balls.
After being bowled by an off-cutter from Zaman Khan in the eighteenth over, the opener was eventually undone. Khan then cheered the New Zealand batsman as he left the field.
Pakistan, in response, never appeared to be approaching the necessary 11.25 run rate.
They lost four wickets for just 39 runs after reaching 95 for two in the eleventh over due to a string of unfortunate incidents.
In a late cameo, Mohammad Nawaz scored 28 off 15 deliveries, but Babar Azam top-scored with 58 off 37 deliveries.
The final two games are on Friday and Sunday in Christchurch.
