Pakistan ended the second day having collapsed to 57 for four in reply to England's first innings 589 for eight declared, a huge deficit of 532 runs.
Root's Test-best 254, just the sixth double century scored in 132 years of Test cricket at Old Trafford, saw him bat for more than 10 hours.
Woakes, who earlier on Saturday made a brisk 58, then underlined his growing all-round credentials with three for 18 in six overs as he dismissed Mohammad Hafeez (18), Azhar Ali and nightwatchman Rahat Ali (both one).
Left-handed opener Shan Masood (30 not out) and Pakistan captain Misbah-ul-Haq (one not out) got through to the close.
England resumed on their overnight 314 for four, with vice-captain Root 141 not out after he had shared a second-wicket stand of 185 with skipper and fellow senior batsman Alastair Cook (105).
Although sent in as a nightwatchman, Woakes showed his batting class on Saturday during a boundary-filled fifty that saw him outscore Root in in a fifth-wicket partnership of 103.
Two not out overnight, Woakes -- who has scored nine first-class hundreds -- was soon demonstrating a fundamentally orthodox batting technique with a succession of fours off Rahat.
Mohammad Amir, another of Pakistan's left-arm quicks, was uppercut for six high over third man by Woakes.
Root had not given 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. That gave Shah then-innings figures of one for 139 in 38.4 overs -- a marked contrast to his man-of-the-match return of 10 for 141 during Pakistan's 75-run win in the first Test at Lord's last week.
Root went past his previous best of 200 not out against Sri Lanka at Lords two years ago with an extravagant reverse-swept four off Shah.
Poor fielding has been a feature of Pakistan's play this series and Jonny Bairstow, last man out for 58, was reprieved on nine when he edged Shah only for wicket-keeper Sarfraz Ahmed to fumble the catch.
Root was eventually dismissed when he skyed Wahab Riaz legside and Hafeez, running in, held a good catch.
In total, Root batted for 10 hours 18 minutes, facing 406 balls, including 27 fours.
Three Pakistan bowlers conceded more than 100 runs each, Shah coming back down to earth after his Lord's display with one for 213 in 54 overs.
James Anderson, returning on his Lancashire home ground after missing the first Test with a shoulder injury, took the new ball.
But it was second-change Woakes who did the damage in a spell of three for 14 in 30 balls.
The paceman had Hafeez, carelessly opening the face, caught by second slip Root and the caught and bowled Azhar off a chipped drive.
Ben Stokes, back following a knee injury, then had the experienced Younis caught down the legside by wicket-keeper Bairstow for just one.
Woakes then removed Rahat when the nightwatchman fended a well-directed bouncer to Gary Ballance at short leg.