The 34-year-old Lancashire swing bowler, England's highest Test wicket-taker with 462, moved 12 points ahead of India spinner Ravichandran Ashwin.
Anderson topped the standings for the first time in his career in May, after taking eight wickets against Sri Lanka.
England's win in the third Test gave them a 2-1 lead in a four-match series.
England's James Anderson has returned to the top of the Test bowling rankings after match figures of 4-85 in Sunday's victory over Pakistan at Edgbaston.