Brook smashed spinner Mohammad Nawaz for his 14th boundary to bring up his second century of the series after scoring 153 in the first Test.
He also hit a six before being caught by off-spinner Zahid Mahmood, who took 3-52.
England resumed on 202–5 and added 73 runs before folding an hour before lunch.
Ben Stokes scored 41 and put on 101 for the sixth wicket with Brook, before England lost their last five wickets for just 19 runs.
Ahmed’s second innings figures were 4–120.
England won the first Test in Rawalpindi by 74 runs.