Root, who had batted for 10 hours, was a Test-best 226 not out.
That meant the England vice-captain had surpassed his previous highest score at this level of 200 not out against Sri Lanka at Lord's two years ago.
Root's Yorkshire colleague Jonny Bairstow was 32 not out.
England resumed on their overnight 314 for four, with Root 141 not out after he had shared a second-wicket stand of 185 with skipper and fellow senior batsman Alastair Cook (105).
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Woakes was the dominant partner in a fifth-wicket stand of 103 with Root.
Two not out overnight, Woakes -- who has scored nine first-class hundreds -- was soon demonstrating a fundamentally orthodox batting technique.
When Rahat Ali, one of Pakistan's trio of left-arm quicks along with Mohammad Amir and Wahab Riaz, dropped short, he was cut for four by Woakes.
Next ball, when Rahat over-pitched, Woakes cover-drove him for another boundary.
There was a brief hold-up when Woakes was struck on the right arm by Rahat.
Meanwhile a single off Rahat saw Root to 150 in 269 balls including 18 fours.
The Yorkshireman had batted for six hours without giving a chance on Friday but on 155 he had a reprieve when an outside edge off leg-spinner Yasir Shah just carried to slip.
But Younis Khan was slow to react to the difficult low catch.
Woakes's 104-ball innings, which included eight fours and a six, ended when he chipped a return catch straight back to Shah to leave England 414 for five.
Stokes was originally given not out by on-field umpire Kumar Dharmasena.
A protracted review suggested there was not clear evidence to overturn his call but third umpire Joel Wilson eventually decided to reverse the decision much to all-rounder Stokes's evident surprise.
Poor fielding has been a feature of Pakistan's play this series and Bairstow was reprieved on nine when he edged Shah only for wicket-keeper Sarfraz Ahmed to fumble the catch, after several juggled attempts.