His 59th minute goal with the help of a goalkeeping error by Alan Marriott settled a keenly contested encounter, the result of which helped to ease Boston's plight in the lower reaches.
The early stages saw little in the way of clear openings as both sides adopted a cagey approach.
The best moments for Boston were off-target snapshots by Dany N'Guessan and Anthony Elding, while a 12th minute scramble in the home six-yard box gave Lincoln the sniff of a chance until keeper Andy Marriott dropped on the ball.
Boston threatened in a more positive fashion with two corners in the 21st minute and from the partially cleared second flag-kick, David Galbraith crossed for Elding to flick a header into the hands of Alan Marriott.
Ten minutes later a low ball in from the left by Tim Ryan gave Boston another opening, but Elding slid in to balloon the ball over from eight yards.
Lincoln hit back and on 35 minutes a 25-yard free-kick was tapped aside by Nicky Eaden for Paul Mayo to see a swerving drive saved at full stretch by Andy Marriottt.
Moments later the home keeper was again in action when sprawling to hold an angled cross-shot by Jamie Forrester.
Back at the other end, Green cut in from the right for Boston but saw his low 15-yard drive smothered by Alan Marriott.
Then, in the dying moments of the half, the Lincoln keeper denied Elding while Green saw and 18-yard shot cleared off the line by Lee Beevers.
Two minutes after the interval Boston went close again when Ryan swept a dipping 25-yard shot inches past a Lincoln upright.
Almost immediately at the other end, the visitors missed a glaring chance when Beevers sliced wide with the goal at his mercy following a Jeff Hughes free-kick into the danger area.
Boston though took the lead in the 59th minute when a Stewart Talbot forward pass found Green and his 12-yard shot trickled into the net after squirming under Alan Marriott's left hand.
Lincoln thought they had equalised four minutes later, but although Forrester forced the ball home, the effort was ruled out for offside.
Shortly afterwards Boston pressed again when Ryan crossed from the left, but Elding's near-post header flew too high.