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Briscoe claimed the checkered flag at Phoenix Raceway for Stewart-Haas Racing, winning his first NCS race in his 40th start.
Briscoe also becomes the 200th different race winner in NASCAR Cup Series history.
Ross Chastain and Tyler Reddick, who were also hunting their first Cup win, finished second and third. Ryan Blaney (Stage 2) and William Byron (Stage 1) each earned a playoff bonus point for their stage wins.
The race was slowed by eight cautions. There were six different leaders and 14 lead changes.