Brook's century gives England edge in third Pakistan Test
England took an improbable 50-run lead on the back of Brook's innings before they were bowled out for 354 and Pakistan cut the deficit to 29 at the close of play.
Pakistan's openers Abdullah Shafique and Shan Masood were batting on 14 and three respectively as the home side ended the day on 21 for no loss.
Brook's 111 revived England's chances of becoming the first team ever to clinch a 3-0 series sweep in Pakistan after the visitors were teetering at 145-5.
England lead the three-match series 2-0 after a 74-run win in Rawalpindi and a close-fought 26-run victory in Multan.
After Pakistan's spinners knocked over the English top order, Brook and wicketkeeper Ben Foakes amassed 117 for the sixth wicket, and brought England within touching distance of Pakistan's first innings 304.
Brook drove spinner Abrar Ahmed for his eighth boundary to reach his third career hundred following up his 153 in the first Test and 108 in the next.
After the close of play, the 23-year-old Brook revealed he had set a goal of scoring two centuries during the tour.
"I said to one of my mates I'd like to get two before I got here, so it feels very nice to go one better," said Brook, who played for Pakistan Super League winners Lahore this year.
On his crucial sixth wicket partnership, Brook said the key was staying at the crease.
"Ben (Foakes) didn't look like he was going to get out. We just knocked it around for as long as we could. We were just trying to build a partnership."
In all Brook cracked eight fours and three sixes before he was trapped leg before to become debutant paceman Mohammad Wasim's first Test wicket.
Brook has now scored 468 runs -- beating David Gower's 449 in 1984 -- for the highest series total by an England batter in Pakistan.
He also equalled Mohammad Yousuf's record of three hundreds in successive matches in an overseas series. The Pakistani batter hit three centuries in England in 2006.
Undone by spin
Pakistan's spinners Nauman Ali and Abrar Ahmed had England in a tight spot after the first session. The pair claimed the first four English wickets and finished with 4-126 and 4-150 respectively.
England were struggling at 145-5 soon after lunch when Ben Stokes (26) attempted a third run which Brook turned down only to see his skipper stranded.
After Brook fell, Foakes added another 51 alongside Mark Wood for the eighth wicket.
Nauman then dismissed Foakes while Ahmed accounted for Wood and Ollie Robinson for 29.
The Pakistan spinner was optimistic about getting a win in the match despite England's recovery.
"We still have a good chance because they have to play the fourth innings," said Nauman.
"If we give them a 200-250 target then we have a good chance because there will be turn and low bounce in the coming days."
In the morning session, Nauman removed Ben Duckett and Joe Root off successive deliveries.
With the National Stadium pitch offering turn, left-armer Nauman trapped Duckett (26) leg before and had the experienced Root caught low in the slip by Agha Salman for nought.
Pope stood firm amidst the dual wicket fall, reaching his 11th fifty before he was bowled for 51 by Ahmed, who added to the wicket he took on Saturday.
