Rangers were booed off by the angry home fans after being second best to the O's for most of the match.
Orient keeper Stuart Nelson saved Martin Rowlands' early shot and saw Stefan Bailey's volley fly over his crossbar, but it was the visitors who looked more likely to score in the first half and then dominated the second.
Boyd had an effort saved by goalkeeper Lee Camp and went close again in the 20th minute, when he got in behind the QPR defence but shot wide.
Rangers breathed another sigh of relief when winger Wayne Corden beat Zesh Rehman and pulled the ball back for John Melligan, who fired over.
Rangers made a determined start to the second half and midfielder Nick Ward sent a 20-yard curler wide of Nelson's right-hand post.
But Orient stepped up a gear and took the lead on 55 minutes.
Boyd beat the Rangers offside trap and in trying to control the ball he inadvertently laid it into the path of Demetriou, who slotted past Camp.
Rangers had Camp to thank for not falling further behind six minutes later. The England Under-21 international did brilliantly to palm Wayne Gray's close-range effort onto the bar after the forward had connected with Demetriou's cross.
However, Camp was unable to rescue Rangers when Danny Cullip pulled down Gray in the box and Boyd calmly converted the resulting penalty.
Rangers were given hope when Rowlands slammed in the loose ball following Tamika Mkandawire's last-ditch challenge on Ward.
But Orient held out for a deserved win and almost grabbed a late third through Gray, who shot wide of Camp's near post.