It was a result that followed a week of turmoil at the club, after a takeover that had seen manager Neil Thompson depart in advance of the expected return of Steve Evans when his FA ban ends in two weeks time.
Home keeper Paul Bastock twice dropped easy catches and had to be rescued by his defenders. But there was nothing he could do to prevent Leon Britton from slotting in from 15 yards following Brad Maylett's right-wing cross on 14 minutes.
The Pilgrims had a few forays in reply, notably down the flanks through Mark Angel and Lee Thompson, but the Swansea defence stayed resolute.
Boston lost the services through injury of their main midfield influence, Neil Redfearn, on the hour and found it increasingly difficult to put any cohesive moves together.
They tried to summon a late rally and twice Duffield went close with headers from Bennett crosses, the second of which was tipped onto the bar by Freestone.
Boston's efforts though yielded reward on 87 minutes when Stuart Douglas headed Thompson's cross from the right back across goal and Boyd pounced to fire in from eight yards.
The result doesn't affect the league table positions. Boston consolodate their place sixth from bottom with 33 points, while Swansea stay 10th on 42 points, 9 off a play-off place but with two games in hand.
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