Pakistan in Christchurch on Tuesday in the tri-series. Allen blasted six sixes in a tally of 62 off 42 balls as the Black Caps chased down 130-7 with ease at Hagley Oval as New Zealand claimed their second win of the series.
The hosts' victory leaves both Pakistan and New Zealand on two wins and a defeat each, with the Black Caps next facing Bangladesh on Wednesday, also in Christchurch.
The three nations are using the week-long tournament to fine tune for the T20 World Cup in Australia later this month The Black Caps avenged Saturday's defeat to Pakistan with an improved bowling performance before Allen and Devon Conway quickly found their stride in an opening partnership of 117 to set up victory.
After Allen was stumped by Mohammad Rizwan, Black Caps captain Kane Williamson replaced him at the crease to eventually claim the winning single as New Zealand won with 23 balls to spare.