Arsene Wenger's team had enjoyed a famous 2-1 win over Spanish champions Barcelona in their Champions League last 16 first leg on Wednesday, but they were brought back down to earth in east London as Orient substitute Jonathan Tehoue cancelled out Tomas Rosicky's opener.
Wenger made 10 changes from the line-up that beat Barca, with 18-year-old Spanish centre-half Ignasi Miquel making his debut, and Orient were never overawed against the understudies.
Arsenal midfielder Rosicky broke the deadlock with a header from Nicklas Bendtner's cross in the 53rd minute.
But Orient earned a money-spinning replay at the Emirates Stadium when French striker Tehoue skipped past two defenders and smashed a powerful shot past Manuel Almunia's weak attempted save in the 89th minute.
Whatever happens in the replay, the players are due a fortnight in Las Vegas at the invitation of Orient's flamboyant owner, snooker promoter Barry Hearn, who had promised them the trip should they either win or get a draw.
The winners of the replay will face Premier League leaders Manchester United at Old Trafford in the quarter-finals.
Wenger said: "We have played the game with the right attitude and could not fault our fighting spirit, but you also have to give credit to Leyton Orient because they never gave up.
"Overall it is a disappointment, but we are still in the competition. The most negative side of our result is one more fixture and in fairness, that is not what we needed."
Orient boss Russell Slade added: "I thought we were going to lose with a bit of dignity but that's our seventh game in the FA Cup.
"We nearly went out in the first round, and to hang in there... It's the same in the league, it's one defeat in 21. You have to be happy with that."
Elsewhere on Sunday, Patrick Vieira fired Manchester City into the fifth round as the French midfielder's double inspired a 5-0 rout of Notts County in a fourth-round replay.
Vieira, a four-time FA Cup winner with Arsenal, was on target in each half at Eastlands and Carlos Tevez, Edin Dzeko and Micah Richards also scored late on as Roberto Mancini's side booked a home clash with Aston Villa.
Mancini's men took the lead in the 37th minute as Vieira's header from David Silva's corner deflected in off Krystian Pearce.
Vieira struck again in the 58th minute with another header, this time from Alexandar Kolarov's corner.
Tevez came on to score in the 84th minute, while Dzeko netted in the 89th minute and Richards completed the rout in the final moments.
"In the first half an hour Notts County played very well," Mancini said.
"It was an important win. I think for us it (the FA Cup) is important.
"We started the game so slowly because when you play every three days, it is difficult to play 100 percent in every game. But after we scored it changed the game."
Bolton beat Fulham 1-0 at Craven Cottage in the fifth round to secure a quarter-final clash at Birmingham.
Fulham were unbeaten in their last six games, but they fell behind in the 19th minute when Croatian striker Ivan Klasnic pounced on a poor clearance to drill a fine volley past Mark Schwarzer.
It capped a good day for Klasnic, who scored the winner against Wigan in this week's fourth-round replay, as the Bolton star also learned he would not face charges after he was arrested on suspicion of rape in October.
Bolton manager Owen Coyle said: "We knew from the outset he had done nothing wrong. Ivan was in a bad position because we couldn't really say anything because of the extent of what was involved.
"He has tried to deal with it with a smile on his face. He probably felt his family were hurt more than himself because he knew he had done nothing wrong.
"We are glad it is away and hopefully we can see the best of Ivan now in the run-in."
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