Kane collected a pass from midfielder Ross Barkley in the 64th minute and beat goalkeeper Dario Melo with a low shot at the near post to give England its second point of the tournament after drawing 2-2 against Iraq in its opener.
Nicolas Castillo had put Chile in front from the penalty spot in the 32nd after Daniel Potts brought down Chile winger Angelo Henriquez in the Group E match.
Iraq was playing Egypt in the group's late game on Wednesday.
In Group F, Uruguay earned its first points by beating New Zealand 2-0 with goals from Giorgian De Arrascaeta and Nicolas Lopez.
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