United had the better of the opening half but the nearest they came to scoring was when they had a 33rd-minute penalty appeal turned down.
The visitors then appeared to be happy to sit back and soak up the Lincoln pressure as they held out for an away point.
Boston created the first chance of a mistake strewn match in the 23rd minute when Julian Joachim put Chris Holland clear, but from 10 yards the midfielder saw his shot saved by Lincoln keeper Alan Marriott.
Then came the penalty decision when Joachim's strike partner Lawrie Dudfield went down in the six-yard box under a challenge from Gareth McAuley.
Boston appealed for a spot-kick but referee Scott Mathieson waved play on.
Three minutes later Lincoln almost scored at the other end when the impressive Luke Foster played in Derek Asamoah.
The striker hit a first-time shot but Boston's teenage goalkeeper Conrad Logan, on loan from Leicester City, got down well to push the ball away.
United skipper Stewart Talbot wasted a half-chance just before the break when he blasted a shot over from 25 yards.
Then Paul Ellender got between two defenders to meet a Danny Thomas free-kick but headed wide from close range.
Lincoln stepped up the pressure and were inches away from taking the lead in the 52nd minute. Gary Birch served Richard Logan, who beat the visitors' offside trap but his shot from the edge of the box scraped the post.
Then a long throw from Lee Beavers found the head of Richard Logan but his effort was palmed away by Conrad Logan.
Lincoln brought on Marvin Robinson in a bid to pep up their attack but still could not get the breakthrough.
Ten minutes from time Nat Brown smashed in a low drive from 20 yards but Conrad Logan made a comfortable save.
In stoppage-time Beavers put Asamoah in the clear but the striker blasted his shot into the side netting.