Brook's century was critical (108) in giving England a big lead, while captain Ben Stokes was dismissed for 41 off 51 balls.
The tail failed to wag for England, with Ollie Robinson (3), Mark Wood (6), Jack Leach (0) and James Anderson (4) all skittled out cheaply.
Pakistan spinners Abrar Ahmed and Zahid Mahmood shared seven wickets between them.
Debutant Abrar finished with a match haul of 11 wickets.
England, on their first test tour of Pakistan since 2005, are 1-0 ahead in the three-match series.