Cook, who won the toss, made 105 and shared a second-wicket stand of 185 with vice-captain Joe Root, who at stumps was 141 not out in a first-day total of 314 for four.
Pakistan had gone 1-0 up in the four-match series with a 75 run-win in the first Test at Lord's last week -- a match where no England batsman made a century.
Shahzad, Umar unlikely for England ODIs, T20Is
The first Test also saw Pakistan leg-spinner Yasir Shah take 10 wickets.
But it was a different story on Friday, with Yasir wicketless in a return of none for 111 in 31 overs.
Cook's century saw him extend his own England Test record to 29, but it was his first hundred at this level in 20 innings since a mammoth 263 against Pakistan in Abu Dhabi in October.
"It's been a while since I scored a hundred for England," Cook told reporters.
"First-innings runs, as always in any Test match, are vital."
Cook's hundred saw him draw level with Australia hero Don Bradman's Test tally of 29 centuries.
Series not over yet, says Misbah
"I can't really compare that, when he did it in half the games or even less ... so it's just nice to get past 28 [hundreds]," said Cook, in his 131st Test compared to Bradman's 52.
Root, twice out because of poor shots at Lord's, did not give a single chance in more than six hours' batting on Friday.
"I've felt in good touch all summer, [but] I've found some stupid ways to get out," said Root. "I worked really hard today, to graft -- maybe not score at the rate I have done previously over the last couple of years, but if that's what it's going to take to score big hundreds that's what I'm going to have to do."
Root added playing more straight bat shots had taken the "risk out" of facing Yasir.
Pakistan bowling coach Mushtaq Ahmed said Yasir, who has enjoyed a meteoric rise to the top of the world bowling rankings, with this match just his 14th Test, had struggled with trying to live up to his Lord's display. "Sometimes the expectation does put you under pressure," explained Ahmed.
Asked if Yasir had bowled too quickly, Ahmed, himself a former Pakistan leg-spinner replied: "Yes, exactly. I think the ball wasn't coming nicely from his hand.
"On a first-day pitch, the margin of error for a leg-spinner against good players like Joe Root and Cook is very small.
"I always believe that as a good bowler you have to bowl good overs against good players to get them out. He didn't do that today, but he will come out [to bowl] tomorrow, he's a strong guy."
Mohammad Amir, after a generally polite reception at Lord's where he made his return to Test cricket after six years out following his 2010 spot-fixing crime at the 'home of cricket', found himself subjected to repeated taunts by spectators on Friday.
The left-arm quick had been given a five-year ban for deliberately bowling no-balls and, as the day wore on, there were ever louder crowd shouts of "No ball!" in his delivery stride.
"He handled them very well," said Ahmed of the 24-year-old, who led Pakistan's attack with two for 63 in 20 overs. "He's a mature guy and just focuses on his bowling."
Meanwhile, Cook insisted: "I actually didn't notice them [spectators)] calling no-balls -- I suppose that's probably quite a good sign, that I'm thinking about more important things."
The left-handed opener added: "I said at the beginning of the series that at some stage that might happen.
"There's got to be some consequence a little bit...of what he did.
"But I think the most important thing is the way both sides, so far in the series, have got on and played good cricket."
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