At stumps Pakistan were 12 without loss for in their second innings, a deficit of 330, after England had declared their first innings on 461 for nine with Bell 106 not out following left-hander Cook's Test-best 127.
But England's joy was tempered at when pace spearhead Stephen Harmison, who took six wickets in the first innings, was forced to leave the field early with a side injury picked up after bowling just two overs as Pakistan began their second knock.
Cook's hundred - his third in only his seventh Test - followed his 105 in the drawn series opener at Lord's where Bell made 100 not out.
"It was a decent pitch to play on. The second new ball nipped around a bit, but it's been a good wicket overall. It's nice if you can get in, because you can definitely score on it," said Cook.
Bell said that he felt under pressure having to wait to bat.
"I didn't quite expect to come in and play like that after sitting and watching the guys," he admitted.
"When you've been waiting four hours at Lord's and two hours today watching runs being churned up it puts pressure on you, but I enjoyed the challenge.
"From ball one it felt fantastic. I've been working hard on my starts, my footwork is going well and I feel in good form."
Earlier this season Kevin Pietersen called on England's younger players to step up to the mark and 21-year-old Cook and Bell, 24, certainly did that.
At tea, England were 357 for seven with Bell 40 not out.
Bell was on 59 when No 10 Harmison came to the crease. But the fast bowler, whose six for 19 ripped the heart out of Pakistan's meagre first innings 119, then showed his batting ability.
He made 26, with four fours, adding 73 for the ninth wicket with Bell.
Warwickshire right-hander Bell's cut four off leg-spinner Shahid Afridi took him to a fourth Test hundred, and third against Pakistan, off 127 balls with one six and 13 fours.
Harmison eventually fell to leg-spinner Danish Kaneria, who bowled 37 overs for a solitary wicket. Monty Panesar was three not out.
Bell, who in common with Paul Collingwood, Cook and England stand-in captain Andrew Strauss had made a century at Lord's, earlier completed a 61-ball with seven well-struck fours.
Tailender Matthew Hoggard hung around for 30 balls before he was lbw, playing no shot, to leg-spinner Shahid Afridi.
That left England 384 for eight.
But Bell kept playing his shots, lofting Afridi for a superb straight six and later drove him through extra-cover for four.
However, Harmison, quite capable of clean hitting, struck Umar Gul over mid-off for four before pulling Mohammad Sami to the mid-wicket fence.
Bell then went into the 90s with another textbook shot, a cover-driven four off Sami.
Pakistan, who had taken just one wicket in the first session when Pietersen fell for his overnight 38, took the new ball in the 87th over in a bid to make further inroads with England then 286 for three.
Their decision was vindicated six balls later when Collingwood pulled Gul straight to Sami at square leg.
The Durham all-rounder's 48 featured two sixes and three fours and together with Cook he put on 119 for the fourth wicket.
Soon afterwards left-hander Cook was lbw to the hard-working Gul.
He batted for more than five-and-a-half hours, facing 260 balls with 18 fours having resumed Friday on 65 not out.
Wicket-keeper Geraint Jones then hooked Sami for six.
But a ball later he was hit on the ring finger of his right hand and next ball Jones, who later had to have ice treatment, was lbw after he tried to pull a full length Sami delivery and missed.
England were now 321 for six, Bell their last remaining recognised batsman.
They resumed Friday on 168 for two after Harmison and left-arm spinner Panesar (three for 21) helped dismiss Pakistan for just 119 on Thursday.
On an increasingly benign pitch Collingwood, whose 186 at Lord's was his Test-best score, used his feet to drive Kaneria for six.
At the other end, Cook square-cut Abdul Razzaq behind point for four and a cover-driven boundary off saw him to 97 before a two off Afridi saw him to his hundred.
Pakistan 1st Innings 119 (S Harmison 6-19, M Panesar 3-21)
England 1st Innings (overnight: 168-2)
7-357, 8-384, 9-457
Pakistan 2nd Innings
To bat: Younis Khan, Mohammad Yousuf, Inzamam-ul-Haq, Faisal Iqbal, Abdul Razzaq, Shahid Afridi, Mohammad Sami, Umar Gul, Danish Kaneria
Umpires: Steve Bucknor (WIS), Simon Taufel (AUS)
TV umpire: Ian Gould (ENG)
Match referee: Ranjan Madugalle (SRI)