Chasing a target of 165, Brook looked in imperious form on a pitch favoured spin with Eland's next highest score came from Will Jacks, batting at number 7, with 28.
England's top-order were rocked by seamer Shaheen Shah Afridi (4-30), who took the scalps of Phil Salt, Jos Buttler and Jacob Bethell, to slip to 35-3.
Brook, who promoted himself to number 3, was immense though as he struck four sixes and 10 fours in what was his maiden T20I hundred.
England then suffered amini-collapse when the skipper lost his wicket with 10 runs still needed but eventually got over the lone with five balls to spare.
Pakistan had earlier suffered a collapse of their own, from 122-3 to post a total of 164-9 in their 20 overs.
Sahibzada Farhan struck 63 from 45 balls while there were middling contributions from Babar Azam (25), Fakhar Zaman (25) and Shadab Khan (23).
England spinner Liam Dawson initiated the collapse with figures of 3-24 while seam dup Jofra Archer and Jamie Overton took two wickets apiece.
Pakistan have appointed former captain Sarfaraz Ahmed as new head coach and also selected four uncapped players in the squad for the Test series in Bangladesh next month.
Ben Stokes admits he got "quite lucky" after a suffering a "pretty nasty" facial injury that has ruled the England Test captain out for at least the next month.
England Test captain Ben Stokes is "very confident" that he and head coach Brendon McCullum will work well together when the home series against New Zealand gets underway in June.
Harry Brook will play two first-class matches ahead of England's home Test series against New Zealand in June while Joe Root will take part in three games, county side Yorkshire have confirmed.
