The former England skipper passed retired Australian great Ricky Ponting when he reached 120, having overtaken India's Rahul Dravid and South Africa's Jacques Kallis earlier in the day.
The 34-year-old, appearing in his 157th Test, went past Ponting's tally of 13,378 runs with a single on the offside as the crowd stood to applaud him and chanted "Roooot".
Minutes later, England reached tea on the third day at 433-4 in reply to India's first-innings score of 358.
India's Sachin Tendulkar is safe in top spot for now, having scored a mammoth 15,921 runs in 200 Tests, but Root has time on his side.
England are 2-1 up in the series, with the final Test at the Oval starting next week.