Murali Vijay (126) and Cheteshwar Pujara (124) stitched together a 209-run stand for the second wicket and the hosts seemed set for a satisfying end to the day before England struck late to reduce them from 318-2 to 319-4.
Vijay was removed by leg-spinner Adil Rashid while nightwatchman Amit Mishra fell for a duck to left-arm spinner Zafar Ansari, 19-year-old debutant Haseeb Hameed taking both catches at short leg.
"It's given us a huge lift in our dressing room," Farbrace told reporters. "When you go the whole day with two wickets, to get two at the end is a real bonus.
"I think it's perseverance to stick to a very disciplined way of bowling all day. We bowled to two outstanding batsmen ... on a very good cricket pitch."
England's plan was to restrict India from scoring freely after they resumed on 63-0, replying to the touring side's 537.
Farbrace felt his team were successful as they restricted India to 256 runs in the day.
"Our plan today was literally to stay outside off stump, make it difficult to score for them, score one side of the pitch and set a field for it," the 49-year-old said. "We were never going to be attacking."
Local boy Pujara made his century in front of his family and friends but was not completely satisfied.
"I was hoping to get a double hundred," said the 28-year-old who has struck two double centuries in his last 38 tests.
"My thinking was because they had so many runs on the board, I did not just want to score a hundred. If I got a double hundred that would have helped the team."
(Editing by Tony Jimenez)
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