Jon Shaw's 18-yard strike rescued a late point for Crawley.
Crawley took an early lead from a Robbie Matthews volley before quick goals from Stacy Long and Michael Gash fired Ebbsfleet ahead.
Guiseppe Sole's 25-yard free-kick then gave the hosts a two-goal cushion before Adam Quinn's close range finish reduced the deficit to 3-2.
Ricky Shakes left-foot shot made it 4-2 before Jon-Paul Pittman's 12-yard shot and Shaw's late goal secured a point.
Ebbsfleet United: Cronin, Stone, Smith, Crooks, Duncan, Long, Hand, Barrett, Shakes (Pooley 89), Gash, Sole. Subs Not Used: Purcell, Ibe, Judge, Ricketts.
Goals: Long 13, Gash 17, Sole 47, Shakes 65.
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Booked: Wright.
Goals: Matthews 4, Quinn 50, Pittman 84, Shaw 90.
Att: 795
Ref: S Beck (Essex).
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