Brook cashed in on some indisciplined bowling from a lightweight seam attack to make 91 from 93 balls on Thursday as England opened a 195-run lead with two first-innings wickets still standing.
It took the Yorkshireman's average in his 12 Test appearances against Pakistan above 85.
Dropped on one at second slip by Salman Ali Agha off Khurram Shahzad, Brook then illuminated a grey, rain-shortened day for his home crowd with an innings containing 13 fours before falling to spinner Ali Usman, who finished with 5-92.
Brook shared a fifth-wicket partnership of 120 with the recalled Dan Lawrence who made 51 from 79 balls.
Lawrence, back after two years in the wilderness, filled the boots of Ben Stokes after his retirement in positive fashion, before top-edging a sweep off Usman.
The pair made the most of the base laid earlier by Joe Root and Jordan Cox.
Root made 66 – his 109th Test innings of 50 or more - and Cox 73, the first of his career, in a stand of 150 for the third wicket.
It was a surprise when Root played across a straight ball from Khurram Shahzad to be trapped lbw, four balls after Cox departed when he misjudged the length of a full ball from Usman to be caught behind.
Cox, given his chance at No.3 by Jacob Bethell's knee injury, hit Khurram for seven fours in the space of 12 balls on the way to a maiden Test half-century.
England, who were helped by some poor ground fielding from Pakistan, closed on 8-366 after Usman dismissed Gus Atkinson and Ollie Robinson with successive balls in the 80th over.
Pakistan, who last won a Test in England eight years ago, are in a tight corner.
With better weather forecast for the remaining three days, they look unlikely to receive much assistance from the elements in their efforts to get out of it.
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