Yado Mambo started his career with Charlton Athletic
Chris Holroyd scored twice for Wrexham either side of the break as they moved to second in the National League.
Holroyd gave the Dragons the advantage at the interval and then doubled their lead with a second half penalty as they kept up the pressure on Dover.
Wrexham are a point behind the leaders after Dover were held to a 1-1 draw by Leyton Orient.
The Dragons are unbeaten in five games in the National League, while Ebbsfleet fall to 12th.
Wrexham manager Dean Keates told BBC Sport Wales: "I thought we did well, the right team won.
"We are over the moon, three points, it is done and we get ready for the next game.
"I thought we were comfortable, we had other opportunities.
"But we are happy with the clean sheet and the three points."
