The Pilgrims' front man shattered Lincoln's 12-match unbeaten run after both sides had enjoyed one half of dominance apiece at York Street.
The first chance of note fell to Boston when, on seven minutes, a Jamie Clarke corner was only partially cleared and Peter Till fired in a low 20-yard shot which Alan Marriott saved well.
Ten minutes later Boston pressed again through Till down the right. He cut inside only to fire straight at Marriott.
In the 26th minute Boston got the breakthrough their efforts deserved.
Clarke floated in a free-kick from the right and Chris Holland headed across goal. Dudfield got in a close range shot which hit the bar and Julian Joachim stabbed in the rebound.
Little was seen of Lincoln as an attacking force with home centre-backs Lee Canoville and Alan White marshalling the home back line to good effect.
The only moment of danger from a City prospective came from three corners, but home keeper Michels Kuipers had a comfortable first 45 minutes.
Lincoln emerged full of fire in the second half and exerted plenty of pressure on the home defence to such an extent that Boston barely set foot in the opposition half for long periods.
But all the visitors had to show for their efforts was an off-target header by Gary Birch and a wild shot wide by Scott Kerr.
Lincoln lost the services of striker Simon Yeo in the 64th minute when he was stretchered off with a leg injury after a challenge by Gary Silk.
He was replaced by Marvin Robinson, whose first action was to chase a ball through the home defence and smash a fierce shot past Kuipers for a 66th minute equaliser.
Boston staged a late rally and in the 90th minute substitute Danny Thomas saw a low cross shot pushed away by Marriott. Then Joachim was also denied by Marriott.
But deep into stoppage time Boston grabbed maximum spoils when Dudfield blasted in from eight yards after White had flicked on a Clarke corner.