Brook was the fourth batter to reach three figures as the tourists ran riot on their way to 506 for four from 75 punishing overs on a flat pitch in Rawalpindi.
Zak Crawley (122), Ben Duckett (107) and Ollie Pope (108) had all got there first, but the Yorkshireman's 80-ball effort was the quickest of all against a weary attack.
Brook was playing just his second Test innings and marked the occasion in memorable fashion in the 67th over, hitting the accelerator in style as he cracked all six deliveries from left-arm spinner Saud Shakeel to the boundary.
The effortless nature with which he worked each delivery into a gap belied the fact that only four other players - Sandeep Patil, Chris Gayle, Ramnaresh Sarwan and Sanath Jayasuriya - have ever managed the feat in the history of the format.
Captain Ben Stokes was seen laughing and hollering his approval from the balcony as the carnage unfolded and Brook's own reaction, laughing openly as he dragged Shakeel's final offering through midwicket, told its own story.
"They were all bad balls, I just tried to put them away," he told Sky Sports with a beaming smile.
"Obviously, I was always going to try and hit the sixth for four. I was probably happier with that over than the hundred to be honest."
Pope was standing watching at the other end when Brook's magical over unfolded and helped him celebrate with a fist bump.
The pair shared a stand of 176 for the fourth wicket and the Surrey player credited the work of head coach Brendon McCullum and skipper Stokes for unlocking new possibilities in the English line-up.
"It was an amazing day and an ideal start to the tour. We've really listened to what Baz and Stokesy have said to us and how they want us to play," he told Sky Sports.
"The best thing is that everyone lived by how the two guys at the top wanted us to play. They want us to entertain people. It's not always about milestones, it's about putting on a show and putting the team in a good position.
"There was 14 off the first over, we just put them under pressure straight away and it looked as though they almost panicked a little bit."