Early optimism gave way to frustration and despair as two first half set pieces and a dismissal for violent conduct for talisman captain Lee Miller left the Cumbrians with a mountain to climb.
The action started at full pace with Carlisle looking the more likely as they won their individual battles across the pitch.
Good pressure from James Berrett forced Cuthbert into a hurried back pass and Lewis Guy was quick to react. He ran into the box and brought a diving save from Jones as he tried to edge the ball into the bottom corner.
Orient responded with some neat football of their own and 24-yard free kick from Lloyd James shaved the outside of the post as Gillespie scramble across to get a touch.
United broke quickly from the goal kick and Josh Gillies opened himself up to have a pop when he linked with Guy on the edge of the area. Jones was beaten but it bobbled agonisingly wide.
The O's started to see more of the ball and they went close when Nathan Clarke was left alone for an inswinging corner. He jumped high and won the header but it dropped behind to safety via the roof of the bar.
But the visitors grabbed the lead moments later when Cuthbert launched a long throw into the box. Kevin Lisbie timed his run perfectly to nip in front of three defenders and get the touch which left Gillespie struggling and stranded.
The afternoon took another turn for the worst on the half hour when Lee Miller and Nathan Clarke went shoulder to shoulder as they chased a reverse pass from Guy. The big defender hit the floor as the pair went shoulder to shoulder and he was eventually stretchered off before leaving the ground in an ambulance.
But it didn't end there as referee Jeremy Simpson pulled Miller to one side and gave him his marching orders for the part he had played in the incident.
Orient took full advantage of their man advantage as they took control of the game and they doubled their lead when they threw men for another set piece. Scott Cuthbert appeared to have acres of time and space as he jumped to thunder his header home from just outside the six-yard box.
The Cumbrians gave themselves hope just before the break when a Gillies shot from a Potts cross cannoned onto Baudry’s raised hand. David Amoo claimed the ball and calmly stroked it into the back of the net from the penalty spot to claim his first goal for the club.
Mark Gillespie pulled off a fantastic double save just before the half time whistle was blown when Lisbie and Mooney took turns at having a pop. A block with the legs from a Mooney drive was particularly important as the back line found themselves outnumbered and stretched.
Carlisle looked sharp at the start of the second half and a top poke from Amoo brought renewed hope as he worked hard to get to the edge of the area. That was followed by a deep free kick from Berrett as he spotted Noble pulling away. He took his time to set himself for a cheeky lob from a very tight angle and he was unlucky to see it drop just wide of the upright.
Reece James got forward well in what was a good spell for the home side and a low, whisked cross had to be gathered with safe hands as Gillies followed in looking for scraps.
Things became stretched at the back as Carlisle tried to make an impact at the other end and that gave the red shirts the chance to exploit some gaps. Mooney should have done better when he had options left and right but he went for glory with a poor effort which Gillespie had covered.
The reprieve was short lived as Odubajo used pace to get to the byline. Mooney kept his eye on the ball and guided his near post header past into the corner of the net.
And Orient extended their lead even further when they launched a long ball forward. It broke for the unmarked Dean Cox and he was able to pick his spot with an emphatic finish.
Substitute Dave Symington hesitated for a split second too long when he found the ball at his feet and the chance was gone as the defenders recovered to make the block.
But it was Orient who looked dangerous and Odubajo had a golden opportunity to add to the scoreline when a half cleared corner fell on the half volley. He opted for power and sent his angled shot into the advertising hoardings.
There was still time for one more goal, though, as Cox latched onto an attempted clearance from Potts. He unleashed a powerful thunderbolt which bounced over the line off the underside of the bar with what was almost the last kick of the game.
“That's put a real dent in all of the optimism and good feeling which was around the place ahead of kick off," manager Greg Abbott said. "We're really disappointed with the goals we conceded because we have to defend better and stronger than that. We’ll get the group together again on Monday and work on it, because if we continue to do that from set pieces then we’re going to make life very hard for ourselves.
"There's not much I can say about the sending off. I didn't see it from where I was and there's not too much point in harping on about it. He’s a big player for us and losing him will be a blow, but we just have to make sure that we get on with it properly.
"There were positives for us but, after a defeat like that, it probably isn't the time to sit and talk about them. Today is not the start we wanted but we will get into work on Monday and make sure we are ready to go again for Wednesday night.”
United - Amoo (43 pen)
Orient - Lisbie (22), Cuthbert (36), Mooney (70), Cox (80, 90)
United - Berrett (9), Noble (35)
Orient - Lisbie (35), Cuthbert (42)
United - Miller (31)
Carlisle United - Gillespie, Potts, Livesey, Edwards, James, Amoo, Noble, Berrett, Gillies (Symington 74), Guy (Beck 74), Miller. Subs - Fleming, Thirlwell, Salmon, Lynch, Brough.
Leyton Orient - Jones, Sawyer, Vincelot, Cuthbert, Baudry, James, Lisbie (Gorman 83), Mooney, Odubajo, Batt (Cox 69), Clarke (Omozusi 34). Subs - Larkins, Lee, De'Reece Vanderhyde, Bartley.
Referee - Mr Jeremy Simpson
Att - 4,951 (301 away fans)