Brook, promoted to number three for the first time in a T20 international, scored exactly 100 off 51 deliveries as England chased down their target of 165 with five balls to spare, despite a late wobble.
After England restricted Pakistan to 164-9, Brook came in second ball of the innings with the score 0-1 after Phil Salt’s golden duck, caught behind off Shaheen Shah Afridi.
Wickets tumbled in the power play but Brook stood firm.
He lifted his side from a precarious 35-3 to 155-6 when he was dismissed, having scored the second fastest century in T20 World Cup history and the first by a team captain.
Brook hit four sixes and 10 fours, surpassing his previous best T20 international score of 81 not out against Pakistan in Karachi four years ago.
He went to the landmark in style, powering Afridi for a six and four to complete his century off 50 balls before being bowled by the left-arm quick next ball.
Afridi, returning to the side, took 4-30 also removing Jos Buttler for two and Jacob Bethell for eight in the power play.
Brook added 45 for the fifth wicket with Sam Curran (16) and even a burst of two wickets from Usman Tariq did not perturb the England skipper who batted with guts and resolve.
Will Jacks helped his skipper towards victory with a brilliant stand of 52, scoring 28 off 23 balls.
Spinner Mohammad Nawaz dismissed Jacks and Jamie Overton in the penultimate over to induce some late nerves, but Jofra Archer hit the first ball of the final over for the winning four.
The defeat leaves Pakistan needing to beat Sri Lanka on Saturday and hope other results go their way to reach the last four after their first match in the Super Eights against New Zealand was washed out.
New Zealand face Sri Lanka on Wednesday in Colombo. (AFP)
Edited by Robert Kemp
