The result lifted Burnley to 12th position on 35 points, eight clear of the relegation zone and one behind 11th-placed Stoke, who failed to score for a fifth successive away league game.
After an uneventful first half at Turf Moor, the night's best action was squeezed into a single minute of action as Boyd broke the deadlock in the 58th minute moments after Marko Arnautovic had come close with a looping header at the other end.
Boyd gave goalkeeper Lee Grant no chance after a dazzling solo run and pass by Jeff Hendrick left the midfielder with time and space to curl a first-time shot from 12 metres into the bottom left corner.