The Pilgrims battled hard and frequently had their high-flying rivals at full stretch, but in the end it the Tigers emerged triumphant to cut the gap on table-topping Doncaster to just one point with a game in hand.
It was Boston who started the brightest of the two sides and they went close three times in the first eight minutes.
First, Stuart Douglas fired over from a Dene Cropper pass. Then Danny Thomas saw a curling 25-yard free-kick tipped away by keeper Boaz Myhill and finally Cropper drilled wide from a Thomas pass.
Hull's best reply was a 20-yard shot off target by Stuart Green.
However, it was the visitors who went ahead in the 18th minute when Stuart Elliott drilled home low from a 25-yard free kick after Paul Ellender had handled.
Nine minutes later more pressure from Hull culminated in Elliott hooking an overhead kick wide. Then a Ben Burgess header from a Lee Marshall cross had home keeper Paul Bastock stretching to save.
Boston replied in the 34th minute as a Mark Greaves header from a Tom Bennett corner was tipped over by Myhill.
Hull again hit back with another set piece move and Junior Lewis tested Bastock with a header after Burgess had flicked on a Richard Hinds free-kick on 37 minutes. Then Bastock performed heroics to block a Danny Allsopp effort at point-blank range.
Boston started the second half at a high tempo and again forced Hull onto the defensive. Only a linesman's flag prevented an equaliser on 52 minutes when Greaves headed in from a Bennett free kick only to be ruled offside.
Seven minutes later Bennett cut in from the left but saw his angled drive flash over the Hull bar.
But just as in the first half the visitors punctured the home defence when Allsopp raced onto a Burgess flick to fire his team into a 2-0 lead.
Boston pulled a goal back on 66 minutes when Ellender fired home low from 16 yards through a crowd of players after a Lee Beevers throw-in had caused problems in the Hull defence.
Boston tried to keep up their attacking work but found the Hull rearguard well marshalled by Marc Joseph and Hinds.
And at the other end a low deflected shot by Burgess tested the agility of Bastock.
As Boston pushed forward in search of an equaliser they were frequently caught on the break but Bastock saved well from Burgess, Allsopp and Green.