Boyd opened the scoring in the first half and then set up Andy Barcham for his first goal for the club, before Luton, under new boss Mick Harford, came storming back with a Keith Keane goal to set up a grandstand finish.
The first half was largely a dismal affair as both sides struggled on the wet surface.
Luton had the first chance when the hugely impressive Matthew Spring saw his shot parried by Orient keeper Stuart Nelson.
Orient finally found some form and Barcham headed over the advancing Dean Brill in the visiting goal, but the effort drifted just wide.
The breakthrough came on 39 minutes when Charlie Daniels and Jason Demetriou combined on the left.
Daniels raced onto Demetriou's lofted pass and keeper Brill came sliding out but lost possession and Daniels continued his run and cut the ball back for Boyd to fire home from six yards.
After the interval, Orient quickly added a second when Boyd released Barcham, who raced through and as the Luton defence retreated he fired home from 12 yards.
But the youngster's joy was shortlived as 60 seconds later he was caught by Chris Perry and had to go off injured.
In a pulsating second half, Keane cut the deficit on 66 minutes when he crashed the ball home from close range after Orient keeper Nelson fumbled Darren Currie's corner.
Luton came storming forward in search of an equaliser, but Orient should have put the game beyond their grasp as first substitute Efe Echanomi and then Boyd rounded keeper Brill only to see their efforts scrambled off the line.
At the other end, Nelson saved well from Spring and Drew Talbot to keep Orient's promotion push on course.