A scrappy first-half littered with petty fouls produced just two chances, both to the home side that visiting goalkeeper Cameron Dawson comfortably dealt with.
The quality of play improved after the break with both teams trading early opportunities as Joe Powell brought a save from Orient on-loan keeper Josh Keeley on his home debut, then a dipping effort from Ollie O'Neill was tipped over by Dawson
The deadlock was broken after 68 minutes when Tom James delivered a free-kick from the left into the penalty box and Happe rose unchallenged to head the ball out of the reach of Dawson..
Sam Nombe immediately came close to an equaliser and Mallik Wilks went close, but a determined Orient side were not to be denied.
Dan Agyei and Ethan Galbraith both went close to doubling Orient's advantage as they finally win for the first time in six home league matches.