Lincoln United racked up their 11th consecutive league win to move level on points with Sherwood Colliery at the top of the table.
But the Poachers can take heart from a performance which saw them push the Whites all the way.
Jordan Nuttell put the hosts ahead after 28 minutes with his 9th goal of the season.
But United were level within 6 minutes through Jack McMenemy.
Martyn Bunce’s side continued to give as good as they got in the second half and it looked as if they’d done enough to earn a point – only for Tobias Liversidge to dash their hopes with an 82nd minute winner.
Even then, Joe Smith was unluckily denied an equaliser when he crashed a powerful header from a corner against the bar in the final minute.
Town: Portas, Worthington (Beeson), Field, Tate (Langford), Ford, Wilson, Bayliss, Maddison, Nuttell (Millar), Smith, Adams (Dakin), unused sub: Limb
Boston Town FC 