Cambridge's rookie goalkeeper John Ruddy emerged as the hero with an excellent penalty save from Matthew Lockwood to ensure the visitors signed off the season with a win.
The 17-year-old, making his football league debut, was beaten by Lockwood's first kick after Andrew Duncan had floored Orient substitute Wayne Purser.
But referee Hegley controversially ordered the kick to be retaken and Ruddy dived to his right and pushed the defender's spot kick away.
But it was referee Hegley who made the headlines as he booked 10 players and sent off Orient's Ciaran Toner on 65 minutes.
The goal that settled the game came early on when Luke Guttridge fired home from 18 yards after Shane Tudor's run and cross from the left had been deflected away.
The referee also ruled out a John Mackie effort in injury time to prevent Orient pinching a point and manager Martin Ling fumed afterwards: "I can't think of anything positive to say about the referee - or our first half performance come to that." The six Orient cautions took them over the 100 mark for the season and Ling added: "Of course it's not good enough and I will take my share of the blame for what has gone before - but not for today.
"It was the worst refereeing performance I have ever seen," he slammed. "Ciaran Toner's tackle was no worse than any of the others and we will appeal against it.
"I don't know why the penalty had to be retaken but I even thought he got the spot kick wrong," added the Orient boss.
Ling even found an ally in United's assistant manager Herve Renard who said: "If I was the Orient coach I would not be happy about the penalty that's for sure.
"But it's a shame the season has come to an end because we have been playing well lately," he said.
The defeat saw Orient end the season with just one win on 15 games as they finished in their lowest ever position.