Sanchez, who has struggled with form and injuries since joining United in January 2018, headed in Chile's third in the 82nd minute.
It was his first goal in any competition since scoring against Arsenal in the FA Cup on 25 January.
Erick Pulgar had given Chile the lead, with Eduardo Vargas scoring twice.
After the match, Chile's record goalscorer Sanchez, who suffered a knee injury and then an ankle problem at the end of the season, said: "For six weeks, I felt worse than I ever have before.
"I struggled in the first half as I felt stifled, but in the second half I was more relaxed and played with more freedom and excitement."
Chile's victory puts them joint top of Group C with Uruguay, who beat Ecuador 4-0 on Sunday.
Japan have been invited to the 12-team tournament in Brazil as guests alongside Qatar.