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Both sides entered the match after opening-round victories, with England defeating Croatia 4-2 and Ghana edging Panama 1-0.
The draw lifted both teams to four points in the group standings, leaving them in a strong position ahead of the final round of fixtures.
England will conclude their group-stage campaign against Panama on Saturday in New Jersey, while Ghana will face Croatia at the same time in Philadelphia.
Despite dominating large periods of the match, England were unable to break through against a well-organised Ghanaian side that defended resolutely throughout the contest.
England, ranked fourth in the world, continue their pursuit of a second World Cup crown since their only triumph in 1966. Ghana, ranked 73rd globally, are seeking to build on their best-ever World Cup performance, a quarter-final appearance in 2010.
England head coach Thomas Tuchel said, “We knew it would be difficult. They defended even deeper than in their first match and set up in a 4-5-1 formation.”