Allen hit six on 62 of 42 while the Black Caps chased away their 131st goal with ease at Hagley Oval.
The win leaves the hosts and Pakistan two victories and one defeat ahead of the Black Cup’s upcoming clash with Bangladesh on Wednesday, also in Christchurch.
The three nations are using the week-long tournament to set the stage for the T20 World Cup in Australia, which begins later this month.
The improved bowling performance saw Pakistan limited to 130 for seven in 20 times before Allen and Devon Conway’s quick-opening partnership secured a comfortable 117 win.
After Allen was baffled by Mohamed Radwan, Captain Ken Williamson saw New Zealand at home with three hits and five balls to spare.
“It was an improvement again from the last game,” Williamson said, referring to New Zealand’s eight-wicket win over Bangladesh on Sunday.
“It was not an easy case, but we played well with the ball.
“The Finn really broke the back of the chase by being so aggressive and Devon did it really well.”
After being undefeated 70 against Bangladesh, Conway hit five times in collecting 49 nos from 46 balls.
“We need to discuss our mistakes before the next match,” Pakistan captain Babar Azam, whose team plays for Bangladesh, said on Thursday.
“We had a bad day, we weren’t up to the mark by hitting us.”
New Zealand bowler Michael Brasswell was named Player of the Match after displacing prolific opening pair Rezwan, at 16, and captain Babar Azam, at 21, in his impressive 11 out of four overs match.
“I was a little lucky with that first with two wide and short that went straight to the fielders,” Brassuel said.
“It was nerve-wracking, bowling for some world class players, but I was happy with the way it turned out.”
Iftikhar Ahmed scored for Pakistan 27, including three fours.
Tim Suthi eliminated Iftikhar and Muhammad Nawaz in the first two deliveries of the final, but Muhammad Waseem survived the triple-ball.