Crawley came from behind to go in at half-time with a 2-1 lead. Moses Odubajo had put the home side in front after 14 minutes before former O's striker Gary Alexander headed the equaliser after 36 minutes.
Alexander's 45th-minute penalty was pushed on to a post by Orient keeper Jamie Jones, but Andy Drury reacted quickly to net the rebound and give Crawley the lead.
Orient went in search of the equaliser after the break, but were stunned when Nicky Adams capitalised on an error by Mathieu Baudry and lobbed the ball over the advancing Jones to give the visitors a two-goal cushion with 15 minutes remaining.
Substitute Marvin Bartley gave Orient faint hope with a scrambled goal six minutes from time, but the visitors held out to record a deserved victory.
"It was a disappointing result after going ahead," he said. "We probably started the better side, got one or two balls into the box and I was reasonably pleased with the start.
"After they equalised, I think we probably had our worst 20 minutes of the season.
"We rolled our sleeves up in the second-half, but then we've made another mistake to go 3-1 down and that proved really costly.
"To be fair to Crawley, they grew into the game, got their two goals in the first-half and would have been delighted to have gone in 2-1 up.
"I've no complaints about the penalty decision because it's caught his arm, but I was more concerned about our defending at that particular time because I think we should have done better.
"It's not like us and that's something we'll have to look at closely.
"It's the second time Crawley have won here in 2013 and they seem to have it over us at this moment in time
"It's a disappointed dressing room because it's a game we feel we allowed to slip away from us.
"It's not been a great performance from us and we have to do better than that."