England were bowled out for 272, adding only 19 runs to their overnight score, as a Yasir Shah-inspired Pakistan took a first-innings lead of 67.
Wickets fell regularly thereafter on a slowish pitch as Pakistan reached 214 for eight for a lead of 281.
"A lead of 300 would be very nice tomorrow," Pakistan coach Mickey Arthur said. "I'm disappointed that none of our batsmen pushed on today."
Pakistan were reduced to 60 for four but valuable knocks from Sarfraz Ahmed (45) and Asad Shafiq (49) kept the scoreboard ticking as Pakistan stretched their lead.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
Shafiq was particularly impressive, striking eight boundaries in his 96-ball innings before missing a straight ball from Woakes and seeing his stumps re-arranged.
Woakes also removed Sarfraz who edged behind to Jonny Bairstow and shortly before the close had Wahab Riaz caught behind for a duck.
He ended with five wickets for 31 as he took his match haul to 11-101 -- the second best match figures for an England player in this decade.
England had resumed on 253 for seven in reply to Pakistan's 339 all out but any hopes of reaching parity or overtaking that total quickly vanished.
Stuart Broad only managed to add six runs to his overnight total before he fell to a full inswinger from Wahab.
The 30-year-old Yasir then trapped Steve Finn leg before for five and, with no reviews left, he had no choice but to walk.
Yasir's figures of 6-72 were the best recorded by a visiting spinner against England at Lord's since Sid Pegler's 7-65 for South Africa 104 years ago.
Debutant Jake Ball was run out by Shan Masood as he looked for a second run to keep Woakes on strike but was short by some distance as Pakistan wrapped up the England tail.
Woakes was unbeaten on 35.
Pakistan made a rocky start to their second innings with Broad having struggling opener Mohammad Hafeez caught by Joe Root at second slip for a duck.
Shan Masood and Azhar Ali steered Pakistan to lunch but both fell to Woakes in the afternoon session, Masood edging an outswinger to Alastair Cook having made 24 and Azhar out lbw after an unsuccessful review.
Moeen Ali then took the prized scalp of Misbah-ul-Haq with the Pakistan captain failing to score.
Younus Khan made a scratchy 25 before being bowled by Moeen but Shafiq was joined by Sarfraz and the pair helped Pakistan into a position of some strength despite best efforts of Woakes.
(Writing by Martyn Herman, editing by Pritha Sarkar)
