Play was paused after an injury to Eagles special teams player Ben VanSumeren on the kickoff at Philadelphia's Lincoln Financial Field.
Players from both teams were on the field and video showed Carter and Prescott in a heated exchange before Carter spit on the Cowboys star.
Carter was immediately assessed a 15-yard unsportsmanlike conduct penalty and thrown out of the game.
It was a blow for the defending Super Bowl champion Eagles. The 24-year-old Carter had 4.5 quarterback sacks and 12 tackles for Philadelphia's top-ranked defense last season.
When the dust settled the Cowboys promptly marched 53 yards in six plays for an opening-drive touchdown, Javonte Williams diving into the end zone for a one-yard score.
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