He clubbed a four off spinner Saim Ayub to become the sixth Englishman to score 300 or more in Test cricket, achieving the feat off 310 balls, with 28 fours and three sixes.
Andy Sandham of England was the first-ever batter to knock a triple hundred in Test cricket, scoring 325 against the West Indies at Kingston in 1930.
Other England batters to score a triple century were Len Hutton (364), Wally Hammond (336 not out), Graham Gooch (333 not out) and John Edrich (310 not out).
Brook has made rapid strides at the international level since making his debut in 2022. He posted three centuries against Pakistan in only his second series which England won by 3-0 margin.
Brook's senior partner Joe Root was unlucky not to reach a maiden triple century as he was trapped leg-before by spinner Agha Salman for 262 soon after lunch.
England had reached 781-5, gaining a lead of 225 over Pakistan's first innings total of 556.