The duo added 171 runs for the second wicket to boost India's hopes of completing the five-match series 4-1.
India lost the opener but bounced back and won the next three matches.
Anderson came 10 short of the historic milestone of 700 wickets in the series and started the final match with 698 wickets.
He started his career in 2003 against Zimbabwe at Lord's and has played 187 matches since then.
Anderson, known as the “Swing King” due to his ability to swing the ball both ways, averages less than 27 and has taken five wickets 32 times in Tests.