In claiming nine wickets, Anderson became the first player to take 100 Test wickets at Lord's and helped England clinch an innings-and-159-run victory in the capital.
Play resumed with England, 1-0 up in a five-match series after their 31-run win at Edgbston last week, yet to bat.
Alastair Cook (21), Keaton Jennings (11), debutant Ollie Pope (28) and Joe Root (19) were the batsmen to have been dismissed, with England 18 runs behind India's first innings total.
And having bowled Vijay for nought in the first innings, it was not long before Anderson had him caught behind by wicket-keeper Jonny Bairstow for his second duck of the match.
Number three Cheteshwar Pujara, who did not play in the first Test, battled for the best part of 24 overs before his resistance was finally breached by a beauty from Broad that nipped back and bowled him through the gate.
Anderson was now just 12 shy of the 563 Test wickets taken by Glenn McGrath.
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Rangana Herath trails behind Anderson, short of just a single wicket, with 99 scalps at Galle International Stadium. England, however, have the cushion of 250 runs and even if the entire day washes out, Joe Root can even declare at the overnight score and give his bowler a great chance of getting 10 wickets of the low-on-confidence Indian batting side on Monday.
Resuming on 357-6, England surprisingly chose to bat on despite extending their lead past 150 on day three when Chris Woakes and Jonny Bairstow shared a partnership of 189.
Speaking after the match, visiting skipper Virat Kohli admitted saying, "We deserved to lose".
"It's not about batting on flat surfaces, I enjoyed playing on surfaces that were given to us, more so when it was an attacking field", he said. To come in and put pressure on the opposition in a tough batting period was good.
This, in the form of the sublime bowling of the master craftsman in Jimmy Anderson and an all-round performance of considerable substance from Stokes replacement in Chris Woakes, was the ideal antidote to Bristol.
England can secure a series win over India in the next Test that starts at Trent Bridge on Saturday. Scoring a hundred and getting on the honour's board is something that'll stay with me a lot. Ultimately little highlighted India's troubles against the moving ball more than the scoreboard at the end of the day - 107 all out - their hopes in this Test disappearing down the drain as fast as the puddles in the outfield had earlier in the afternoon. But like I said, I was a bit nervous out there yesterday.