Rangana Herath trails behind Anderson, short of just a single wicket, with 99 scalps at Galle International Stadium.
As well as reaching the Lord's milestone, the dismissal - Anderson's 96th against India - made him the highest wicket-taker in test matches between the two nations.
England all-rounder Chris Woakes celebrates his maiden test ton as India are trounced at Lord's.
Earlier, India chose to play with two spinners in Ravichandran Ashwin and Kuldeep Yadav, whereas Cheteshwar Pujara had a horrific return to Test cricket.
Ben who? England did not miss their absent friend in the least at Lord's where they moved to the brink of a series win against the best team in the world by dominating an utterly one-sided second Test.
Anderson took his tally for the match to nine wickets by removing Kuldeep Yadav and Mohammed Shami for ducks, before Woakes fittingly finished the job with Ishant Sharma caught at leg slip to put the hosts in firm control of the series.
So often attacking the outside edge, Anderson nipped the ball back to Murali Vijay and he only managed to get a feather through to wicket-keeper Bairstow as his Lord's Test ended with a pair.
His exit gave Anderson, fifth in the all-time standings, his 551st Test wicket.
The top three places all belong to spinners, with Sri Lanka's Muttiah Muralitharan leading the way on 800 Test wickets. He gets to 30 and is now the top-scorer in both the innings for India. yes, he has been India's best batsman in this Test and fair to assume that he will remain by the end of the Test.
Kohli remains the heartbeat of India's batting line-up and having survived a review the delivery before, with England convinced the visitors captain had gloved the ball behind to Jonny Bairstow, he was not so lucky the next ball.
England had earlier declared on 396-7 - with Woakes 137 not out, his first test century - during the opening session of the fourth day.
When Jos Buttler went for 24 - Shami's third leg-before wicket - England looked capable of crumbling again.
Their unbroken sixth-wicket stand was so far worth 99 runs and all the more valuable for the fact that England had slumped to 89 for four on the stroke of lunch.
When asked about the rain-affected conditions, Kohli said that they should not blame the conditions and England deserved to win the game due to their relentless approach on the field.