United were below-par at Grange Lane and fell behind to Gregg Anderson's header four minutes before half-time.
Nathan Jarman doubled the lead within a minute of the restart and wrapped up the victory with a strike nine minutes from time.
Despite suffering a disappointing and deserved defeat, United were still able to contemplate a postive start to the campaign which had yielded seven points from a hugely challenging quartet of opening fixtures.
Ferriby held the upper hand throughout a fairly uneventful first half and ex-Pilgrim Jamie Yates' cross-shot was held by Ashley Timms following a partially cleared corner
United threatened for the first time with Ricky Miller firing in a dipping shot which flew wide from 20 yards after turning away from Danny Hone.
The Villagers took the lead in the 41st minute with ANDERSON wriggling free to head home Yates' corner with real aplomb.
Boston tried to get themselves level but Adam Nicklin was equal to Ben Milnes' 25-yarder.
United emerged for the second half with real aspirations of getting back into the game, but their hopes were extinguished within a minute. Nathan Peat's deep cross from the left was only partially cleared by Carl Piergianni and JARMAN drove the ball back across Timms and into the bottom corner.
The Pilgrims came within a whisker of cutting the deficit moments later, but Nicklin made a brilliant one-handed save to keep out Scott Garner's towering header from an Ian Ross free-kick.
It was nearly game, set and match when Jarman got in behind Conor Marshall, but he curled his shot wide.
Milnes then slammed a shot the wrong side of the post following a strong run forward. Substitute Ben Fairclough had slipped him through.
Ferriby wrapped up all three points when JARMAN swept home Paul Robson's right-wing cross with nine minutes to play.
North Ferriby (4-4-2): Adam Nicklin; Paul Robson, Gregg Anderson, Danny Hone, Nathan Peat; Danny Clarke, Russell Fry, Liam King (Jonathan D'Laryea 76), Jamie Yates; Anthony Wilson (Ryan Kendall 67), Nathan Jarman. Subs (not used): Sam Belcher, Dean Lisles, Antoni Pecora (gk).
Boston (4-3-3): Ashley Timms; Peter Bore, Scott Garner, Carl Piergianni, Netan Sansara (Stefan Galinski 65); Ian Ross, Conor Marshall, Ben Milnes; Spencer Weir-Daley (Ben Fairclough 65), Marc Newsham, Ricky Miller (Charley Sanders 80). Subs (not used): James Reed, Sam Vince (gk).
Referee: David Richardson
Attendance: 618