After veteran spinner Ravichandran Ashwin did the initial damage with 3-64, bowling allrounder Washington ripped through the Black Caps and finished with career-best figures of 7-59 to restrict them to 259 before India reached 1-16 at stumps on a riveting Thursday.
Ravindra Jadeja went wicketless on the day but helped keep the tourists from building on their positive start.
"We communicated a lot. They brought a lot of qualities, skill sets and experience as well. That really helps for someone who is playing along with them. It definitely helped me today," Washington told reporters.
"It's special, isn't it, to be playing in a game that both of them are a part of. I hope that we'll get to play a lot more games together."
Washington was a late addition to the squad after India's eight-wicket defeat in the series opener in Bengaluru and he said he was delighted with how things unfolded for him.
"Right from the start, getting to play this game and coming back to the Test squad, there are a lot of things that I can say mean a lot to me and are very special," added Washington, who replaced Kuldeep Yadav in the eleven.
"I'm grateful. I don't think I'll ever forget this day."
Washington will add extra firepower to India's long batting line-up having scored 152 in a recent domestic game and he said he was looking forward to Friday's action.
"It's going to be exciting," the Tamil Nadu player added.
"Hopefully, we can put a lot of runs on the board."
