Boyd, the former Luton striker signed in the summer, swivelled in the area and beat keeper Asmir Begovic from 12 yards after full-back Aiden Palmer played in the perfect ball.
The goal condemned Bournemouth to their first away defeat of the season as, after dominating the first half, the visitors were swept aside after the interval.
In an instantly forgettable first half both sides managed to carve out just one clear opportunity.
Former England and Spurs midfielder Darren Anderton should have put the visitors ahead on 24 minutes as he found himself in the clear after Jo Kuffour threaded him through, but he was denied by Orient keeper Stuart Nelson.
At the other end, Cherries keeper Begovic pulled off an equally impressive save from close range to deny Wayne Corden after Wayne Gray set up the chance with a run and cross from the right.
The game exploded into life at the start of the second half as Orient created two early opportunities with Sean Thornton and John Melligan both going close.
With Orient in control, Corden clipped an upright following Gray's right-wing cross.
But Bournemouth had their chances too and striker Lee Bradbury saw a header saved by Nelson before Boyd made the all-important breakthrough with his third league goal of the season.
The visitors responded with another Bradbury header, but Orient defended well to hang on to their slender advantage.
As the Cherries threw caution to the wind, Orient almost made them pay in stoppage time as first Boyd shot inches wide and substitute Jason Demetriou went close.