Both sides took turns in having possession in the opening 25 minutes, as the game became a tetchy affair.
However, right at the half-hour mark, Salisbury had the best chance of the afternoon via Josh Hedges.
A shot to the left of the Fleet keeper from inside the area went agonisingly wide after the midfielder was slotted through on goal.
The rest of the first half was dominated by the Whites, as promising counter-attacks troubled the Fleet backline.
Ebbsfleet came out of the interval looking the sharper side, showing why the Kent-based side has won four of their last six fixtures.
The pressure on the Salisbury goal began to mount after some early attempts on goal, and Ebbsfleet were able to win a penalty after Edser was tripped in the box by debutant McIntyre.
Noah Coppin celebrates - Credit John Rose (Image: John Rose)
Samuel then converted from the spot, giving Whites keeper Buse the eyes and slotting it in the bottom left corner.
Salisbury refused to let-up however, with the Whites regaining the lion's share of possession, firing shots at the visitors.
Just as it looked like it wasn’t going to be the hosts’ day, Noah Coppin refused to let the onslaught go to waste, winning a second penalty of the afternoon.
Coppin then converted the penalty with conviction into the bottom-left-hand corner to rescue a point.