Woakes finished unbeaten on 137 when Root declared on the fourth morning then added two further wickets having claimed the prized scalp of Virat Kohli in the first innings.
"Really pleased for Woakesy, on a number of occasions he has shown how talented he is with the bat and that's just down to hard work. Chuffed to bits for him," Root said. "The state of the game and coming back into the side, he has always been a big part of the squad for a long time. It's great to see him take some rewards."
After the first Test had gone down to the wire at Edgbaston, this was as one-sided a contest you could see - dominated by England from the moment they won the toss and James Anderson removed Murali Vijay in the first over. Anderson went on to finish with match figures of 9 for 43.
"Less stress, definitely, a fantastic week from the very first ball," Root said when comparing it to Birmingham. "I thought the bowling unit were exceptional throughout the whole game. I thought we did have conditions in our favour throughout but you still have to perform and we certainly did that. That was really pleasing, then to get that far in front was testament to that partnership in particular from Jonny [Bairstow] and Woakes.
"There are still areas to improve on and that's exciting. We've not played the complete game yet. It's something you are always chasing but hopefully that's in the next three games. Just really pleased for the guys, they've put a hell of a lot of hard work in and there are some who won't get the headlines but you have to do it as a team."
Root also had encouraging words for debutant Ollie Pope who made a positive 28 in his first Test innings and was also a lively presence in the field.
"I thought he played really well. In terms of when we batted, I thought he batted at a very challenging time and to come in and put pressure back on the opposition was a great sign. We've seen it in Championship cricket and to see him fit almost seamlessly into this environment is really pleasing."