Vijay is now India's fourth highest-ranked batsman after Pujara, Virat Kohli (13th) and captain Mahenda Singh Dhoni (27th) in the chart headed by South Africa's AB de Villiers.
Kohli, who flopped in the two innings of the first Test against England, lost three places in the latest list.
Meanwhile, Joe Root became England's highest-ranked batsman after hitting the fourth century of his career against India. He has been rewarded with a jump of 10 places, which has put him in a career-high 16th position.
In the ICC Test bowlers' chart, Indian seamer Bhuvneshwar Kumar and England's Stuart Broad are the biggest movers.
Kumar picked up five for 82 in England's only innings and that has allowed him to break into the top 50 for the first time in his career. He now sits in 46th spot after jumping 27 places.
Broad returned match figures of four for 103, which has helped him rise four places to 10th position.
Ravichandran Ashwin is the only Indian to figure in the top-10 after losing a place to be at eighth.
In the all-rounders' list, India's Ravindra Jadeja retained his number two position.
