The Yorkshire batter, who was brought into the side in the summer in place of the injured Jonny Bairstow, scored 111 to help the tourists post 354 in response to Pakistan's 304.
His latest ton saw him surpass David Gower's total of 449 for the most Test runs scored by an Englishman in a tour of Pakistan, set in the 1983-84 series.
And Brook hopes his exploits will cause the selectors problems for when Bairstow returns from a broken leg.
"Most selectors say they like headaches, so hopefully I've caused a very big migraine," Brook said.
"It's too hard to say at the minute. I think Jonny is one of the best players, if not the best player in the world - he was this summer anyway.
"So for me, he comes straight back in the side. Obviously I'm not selecting the team but he's such a big player for the side and he has been for so many years."
There was one moment of contention during Brook's knock when he left Ben Stokes stranded going for an achievable third run, with the England captain run out for 26.
Stokes' departure left England 145 for five but Brook responded to the incident well, putting on a 117-run stand for the sixth wicket with Ben Foakes.
"It was probably my fault to be honest, I'll take the blame," Brook said about the run out.
"There probably was three there, I was slightly lazy with my running. I was a bit tired to be honest.
"But it was my fault I'll take the blame.
"It probably makes you concentrate a little bit more, actually, when you've been involved in a run out, but obviously I was involved in (one with) Ollie Pope last week and I went on to get a hundred in that game, so maybe I should start something up."
After the first innings of the Karachi Test, Brook averages 73.80 in Test cricket, at a strike rate of just under 100.
When asked about his three centuries in Pakistan so far, he said: "I actually said to one of my mates before I came out here that I would love to get two hundreds out here, so obviously to go one better is a very nice feeling."
Pakistan ended the day 21 without loss in their second innings - trailing by 29 - as they look for a consolation victory in the three-Test series.