Macauley Gillesphey had given the hosts the lead with a thunderous free-kick after only 17 minutes, but an improved display after the restart saw Jay Simpson slot home a 50th minute equaliser to register his 23rd goal of the season.
Subsitute Ollie Palmer then put the O's ahead with a calm finish on the 71st minute, but with six minutes remaining Michael Raynes equalised for the hosts as both sides were forced to settle for a point.
For the O’s longest away trip of the season player-manager Kevin Nolan made two changes to the side that defeated Crawley Town on the weekend.
Jack Payne and Calaum Jahraldo-Martin came into the starting XI in place of Sammy Moore, who dropped to the substitutes bench, and Armand Gnanduillet who was ruled out with a slight injury.
On a wet and windy night at Brunton Park it was the hosts who started the more promising of the sides, though Jay Simpson was almost presented with a chance on the fourth minute when Carlisle goalkeeper Mark Gillespie slipped with the ball at his feet before recovering quickly to clear.
Former Orient striker Jabo Ibehre was leading the line for the Cumbrians and his cross/shot moments later deflected off Mathieu Baudry to find a way into the hands of Alex Cisak.
With 17 minutes played Carlisle made the breakthrough when Jason Kennedy was brought down on the edge of the O’s penalty area before full-back Macauley Gillesphey rifled the free-kick beyond the dive of Cisak and into the top left corner.
The Cumbrians were then presented with a wonderful chance to double their advantage two minutes later when Charlie Wyke was played in behind the O’s defence, but the forward was denied by a terrific stop by Cisak who came flying off his line.
Gillesphey’s strike was the first goal Orient had conceded on the road during Kevin Nolan’s tenure, and with just over ten minutes of the first half remaining Shaun Brisley couldn’t make the most of a half chance as he scuffed Jack Payne’s cross at Gillespie in the hosts goal.
Things hadn’t quite ticked for the O’s throughout the opening 45 minutes and nearly found themselves going into the break two goals down when Kennedy got on the end of Alex McQueen’s lofted a ball into the box, but the midfielder could only glance his header wide of the far post.
Ahead of the second half Orient then made two changes, bringing on Ollie Palmer and Sammy Moore in place of Sean Clohessy and Jack Payne as they changed the formation to a flat 4-4-2.
The double change saw the O’s start the second half brightly, and after Nigel Atangana had blazed an effort over the bar Simpson levelled the tie with a cool finish from the edge of the area to end a run of five games without a goal.
Having grabbed the equaliser Orient then came close to edging in front when a cross from the left dropped out to Moore just inside the box, but despite bringing it down well his shot skimmed the top of the bar.
Player-manager Nolan then curled an effort over from 20-yards, though the Orient defence were then given a reminder of the Carlisle attacking threat moments later as Hallam Hope’s teasing ball fizzed across the six-yard box before going out for a goal kick.
The introduction of Palmer and Moore had certainly proved effective as the pair found themselves involved in several flowing moves, and with 68 minutes played another good attack saw the ball drop to Nolan inside the box but the 33-year-old curled his effort over.
Orient skipper Mathieu Baudry then produced a fantastic challenge to block an Ibehre volley, and on the 71st minute the Frenchman produced an even more crucial challenge to deny Steven Rigg which then resulted in the visitors taking the lead.
Having regained possession from the challenge, the O’s broke quickly and Palmer produced a wonderful touch to knock the ball beyond Mark Ellis before placing a shot beyond Gillespie to send the wonderful 179 travelling supporters into raptures.
As the match entered the final stages Carlisle upped their attempts to find an equaliser and with seven minutes to go Rigg looked set to smash home from inside the box only to be denied by yet another wonderful block from Baudry.
Baudry could do nothing a minute later however as Carlisle forced home a leveller when captain Michael Raynes glanced a header beyond Cisak from six-yards.
Atangana dragged a shot wide in the closing minutes as Orient looked to regain the lead, but there was to be no winner as both sides came away with a point each.
CARLISLE: Gillespie, McQueen (Asamoah 75), Raynes (C), Ellis, Gillesphey, Joyce, Gilliead, Kennedy, Wyke (Rigg 25), Hope, Ibehre
SUBS: Bacon, Hery, Brough, Archibald-Henville, Thompson
GOALS: Gillesphey (17), Raynes (84)
ORIENT: Cisak, Hunt, Baudry (C), Brisley, Binnom-Williams, Clohessy (Palmer HT), Atangana, Payne (Moore HT), Jahraldo-Martin, Nolan, Simpson
SUBS: Grainger, Essam, Shaw, Pritchard, Turgott
GOALS: Simpson (50), Palmer (71)
BOOKINGS: Hunt (40), Palmer (72)
REFEREE: Nigel Miller
ATTENDANCE: 3,721 (179 fantastic Orient supporters)