Anderson picked up three for 52 while fast bowling partner Broad shrugged aside some indifferent recent performances to snatch three for 65.
The pair were well backed up by spinner Moeen Ali who took two for 62 after being banned by the International Cricket Council from sporting the "Save Gaza" and "Free Palestine" wristbands he wore on Monday.
Ajinkya Rahane and skipper Mahendra Singh Dhoni made half-centuries but England, 1-0 down in the five-match series, are in control as they bid to win their first test in 11 outings.
"I've probably been putting too much pressure on myself to take responsibility and I just wanted to get back to enjoying my cricket," Broad told reporters.
"Before this test coach Peter Moores came up to us and said, 'Go and express yourselves', which freed me up a bit. I'm an attacking cricketer but perhaps I fell into a defensive mindset after the tough time we've been going through."
Resuming on 25 for one, the dangerous Broad quickly removed Cheteshwar Pujara (24) and Murali Vijay (35).
Anderson tempted Virat Kohli (39) into a tentative prod outside off stump after lunch and the edge was snapped up by captain Alastair Cook.
Moeen then removed Rohit Sharma for 28, ending a watchful stand of 74 with Rahane.
The spinner also claimed Rahane's wicket following an elegant 54, top-edging a short delivery to substitute fielder Sean Terry at mid-wicket.
The dismissal was another example of India's batsmen being victims of their own downfall as they showed poor shot selection throughout.
"I was really disappointed in the way I got out because I was batting so well and we needed that partnership," said Rahane.
"My focus was 100 percent but I played a bad shot. I'll learn from this and I hope to bat well in the second innings."
Dhoni and Ravindra Jadeja led a brief revival, displaying the counter-attacking style that helped guide India to victory in the last test at Lord's.
When their seventh-wicket partnership had reached 58 Anderson bowled a beauty to Jadeja that nipped back and cannoned into his pads to leave the tourists on the ropes.
Lower-order batsman Bhuvneshwar Kumar, who has hit three half-centuries on the tour, fell to Broad for 19, edging on to his pads and watching the ball loop up to Gary Ballance at slip.
Dhoni struck a patient unbeaten 50 and will resume with Mohammed Shami (four) on Wednesday morning as India look to scrape past the follow-on mark of 370.
Broad and Anderson reached a landmark on Tuesday, combining for their 500th wicket as a test partnership.
It made them only the third pair to achieve the feat, following Pakistani duo Waqar Younis and Wasim Akram and West Indians Curtly Ambrose and Courtney Walsh.
"To be in the company of people like that is a great honour and I think it shows the value of bowling partnerships," Broad said.
"Jimmy and I are constantly talking not just on the field but also in the nets."
Broad said he would not be in favour of enforcing the follow-on.
"I haven't discussed it with Cook but if it were up to me it is 100 percent off limits," he explained.
"From a seamer's point of view you're going back and bowling at opening batsmen so even if you just get a 30 or 40-over rest that's pretty important."
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- Mahendra Singh Dhoni
- Ajinkya Rahane
- International Cricket Council