The torn groin that sidelined top-scorer Jason Walker had not healed and continues to keep the 15-goal hitman out of the promotion-chasing team.
But City were in front after just 10 minutes thanks to a goal from Matty Blair.
York were forced to play the remaining 75 minutes with just 10 men when Scott Brown was red carded for violent conduct.
Nathaniel Pinney equalised for the visitors, but further goals from Blair and James Meredith put York in control.
Calum Willock netted a late consolation for Ebbsfleet.
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