England enjoyed the better of the early stages on Saturday after West Indies resumed on 351-5, still 65 behind on first innings.
Woakes claimed three wickets in a 10-over spell and England took 4-31 overall to leave West Indies 386-9, 30 adrift.
From there, England employed curious tactics. Ben Stokes’ side dropped the field to Joshua da Silva, who had 44, in the hope of exposing number 11 Shamar Joseph.
With Da Silva hammering three sixes and Joseph two of his own, the last-wicket pair added 71 until Joseph was eventually out for 33, leaving Da Silva stranded on 82.
Former England captain Michael Vaughan said the England plan was “questionable” and gave West Indies “a huge chance”.
But Woakes, who ended with figures of 4-84, said: “It’s a period that can cause problems. You just have to commit to the plan you’re going with. It’s not always going to be perfect.
“When the field goes out, as a bowler it’s easy to think you’re not trying to get the set batter out and just think of the number 11. At the same time, you don’t want to give away easy boundaries.
“You don’t always expect the number 11 to hit a couple into the stands. Fair play to them, they played it pretty well. We committed to it for long enough and eventually got the reward.”