What should have been a smooth chase was rattled early on by Mohammad Amir's splendid seam and swing bowling.
The left-armer accounted for Mohammad Hafeez's wicket with a LBW shout on the fourth ball. He had almost removed the right-hander on the first ball when the LBW appeal was turned down by on-field umpire Ahsan Raza.
Kamran Akmal - who had scored a belligerent 88 less than 24 hours ago - fell eight balls later when he skied Sohail Khan to be held safely by Imad Wasim.
England's limited-overs captain Eoin Morgan and Dawid Malan started Zalmi's recovery in the third over when the scorecard read 2-2.
The duo consolidated their side's position by 46 runs before Malan fell to Wasim. Morgan, however, ensured runs don't dry. He registered his first 50-run landmark in the process and ended up with 80 out of 57 balls, his highest T20 score — which yielded him man-of-the-match award.