The first half was relatively nondescript at the Kuflink Stadium, but the Pilgrims came on strongly after half-time and saw good chances go begging through the likes of Jai Rowe, Lennon Wheeldon and Pemi Aderoju.
Defender Connor Teale was handed his United debut and duly helped the Pilgrims keep their first National League clean sheet since September 7.
Jordan Richards cracked an early drive wide for United, while Frankie Maguire lifted an effort too high for the Pilgrims after meeting Sam Reed's cross from the left.
Aidan Stone did well to keep out Luke O'Neill's long-range free-kick, while Toby Edser hooked wide at the back post after Rakish Bingham had flicked on Josh Wright's corner.
United cranked up the pressure after half-time, with Mark Cousins turning Jai Rowe's low drive behind for a corner, before the Ebbsfleet keeper denied Reed - and Wheeldon fired wide at the back post after meeting Jacob Hazel's cross.
Aderoju glanced wide from a Billy Chadwick cross, while O'Neill was well-positioned to divert Rowe's last minute header to safety.
Ebbsfleet (4-3-3): Mark Cousins; Luke O'Neill, Anthony Stewart, Jack Wakely, Ben Chapman (Pape Souare 17); Todd Kane (Maxx Manktelow 46), Josh Wright (Franklin Domi 68), Toby Edser; Aaron Cosgrave (Wes Fonguck 85), Rakish Bingham, Jephte Tanga (Dominic Poleon 68). Subs (not used): Tom Dallison, Dylan Berry (gk).
Boston (4-4-2): Aidan Stone; Jai Rowe, Tom Leak, Connor Teale, Cameron Green; Frankie Maguire (Keaton Ward 82), Jordan Richards, Dylan Hill, Sam Reed (Martin Woods 70); Lennon Wheeldon (Billy Chadwick 70), Jacob Hazel (Pemi Aderoju 65). Subs (not used): Kieran Coates, Sam Osborne, Jake Lovelace (gk).
Referee: Ben Atkinson.
Attendance: 1,563 (260 visitors).
PIC: Chris Bray.