Brook scored a 35-ball 81 not out while Duckett cracked an unbeaten 42-ball 69 after Pakistan won the toss and sent England in to bat at the National stadium.
The seven-match series is tied at 1-1 after England won the first fixture by six wickets while Pakistan took the second by ten wickets, both in Karachi.
Debutant Will Jacks set the platform for England with a sparkling 20-ball 40 with eight boundaries before Brook and Duckett took the attack to the Pakistan bowlers.
Brook cracked five sixes and eight boundaries while Duckett hit a six and eight boundaries as the pair added 139 runs off just 69 balls — a record fourth wicket stand for England in all T20Is.
For Pakistan, leg-spinner Usman Qadir was the pick of the bowlers with 2-48 while pacer Shahnawaz Dahani went for 62 runs in his four wicket-less overs.
England are on their first tour of Pakistan since 2005.
Pakistan remained unchanged from the second game, while England handed a T20I debut to batter Will Jacks and added pacers Reece Topley and Mark Wood to the eleven.
Batter Alex Hales, Luke Wood and David Willey were left out.
The remaining matches are in Karachi (Sunday) and Lahore (September 28, 30 and October 2).
Pakistan: Babar Azam (captain), Mohammad Rizwan, Haider Ali, Haris Rauf, Iftikhar Ahmed, Mohammad Nawaz, Khushdil Shah, Mohammad Hasnain, Shahnawaz Dahani, Shan Masood, Usman Qadir
England: Moeen Ali (captain), Will Jacks, Harry Brook, Sam Curran, Ben Duckett, Liam Dawson, Dawid Malan, Adil Rashid, Phil Salt, Reece Topley, Mark Wood