HOMESTEAD, Fla.—Nothing could stop Jimmie Johnson’s drive into the NASCAR record books. Not even a final, furious push by Carl Edwards.

Edwards led a race-high 157 laps, ran out of gas as he crossed the finish line, but still won Sunday’s season-ending race at Homestead-Miami Speedway. Still, his series-high ninth win of the year wasn’t enough to wrest away the Sprint Cup title.

Johnson locked up his third consecutive championship with a solid 15th-place run, beating Edwards by 69 points to join Cale Yarborough as the only drivers in NASCAR history to win three straight...

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