Perhaps no one will remember the setting, a hearing room for the House Energy and Commerce Committee, or the person who asked the question, a member of the House of Representatives from Illinois. But seven words spoken in the Rayburn House Office Building in Washington on Monday could profoundly affect the country’s most popular sport.

After years of the N.F.L.‘s disputing evidence that connected football to chronic traumatic encephalopathy, the degenerative brain disease found in nearly 100 former players, a top official for the league for the first time acknowledged the link. To many, it was an echo of big tobacco’s confession in 1997 that smoking causes cancer and heart disease.

Representative Jan Schakowsky, Democrat of Illinois, asked during a round-table discussion about concussions whether “there is a link between football and degenerative brain disorders like C.T.E.”

Jeff Miller, the N.F.L.’s senior vice president for health and safety policy, said, “The answer to that is certainly, yes.” His response signaled a stunning about-face for the league, which has been accused by former players and independent experts of hiding the dangers of head injuries for decades.