Orient were pegged back for a point after twice leading at Ashton Gate as the O's made it four points from two tricky away fixtures in four days.
David Mooney had set the O's on their way with a fine curling effort in the first half before Sam Baldock levelled after the restart.
Then against the run of play, Dean Cox put the O's back in front after good work from Odubajo only for the Robins to level almost immediately through an unfortunate Scott Cuthbert own goal.
Orient manager Russell Slade made just one change from the side that won at Swindon on Saturday as Lloyd James returned to action back in his home town whilst Marvin Bartley made way for him dropping to the bench. Whilst Nathan Clarke overcame a slight injury concern to make his 400th start as a pro.
It was Orient who looked to seize control of the early stages and dominated the early exchanges and when Clarke hurled a long throw into the box in the fourth minute, his defensive partner Mathieu Baudry flicked it on to cause panic in the home side’s box but a series of O’s shots were charged down.
You could sense the impatience in the air at Ashton Gate from a home crowd obviously aggrieved at their slow start to the season, however after a sluggish opening 10 minutes, the Robins started to find their feet with Brendan Moloney and Jay Emmanuel-Thomas both fizzing dangerous balls across the face of goal from the right.
Orient’s retention wasn’t as up to scratch as it has been in recent weeks but the almost telepathic understanding between Mooney and his strike partner Kevin Lisbie remained and the pair combined on 21 minutes when the former crossed for the latter who had a header well saved by Elliot Parish.
A minute later however the Irishman broke the deadlock when he once more finished with aplomb as he has done so on so many occasions this season. Dean Cox looked to set free Moses Odubajo with a long ball and the youngster managed to get a shot away that was blocked down into the path of Mooney who bent a curling shot past Parish from the edge of the box.
The home skipper Sam Baldock began to look increasingly isolated up front despite some more patient build up play behind him but the O’s were resilient without the ball and stuck to their shape rigidly to frustrate the home faithful and restrict the Robins to efforts from distance as the home side finished the half the stronger but the O’s took the lead into the interval.
The Robins began the second period with a greater intensity as you'd expect and five minutes after the restart, Emmanuel-Thomas was the first to call Jones into action with a drive from distance.
Orient struggled to get a foothold in the early exchanges but thought they had extended their lead with 10 minutes of the second half played. Cox and James combined from a short corner as the former whipped a ball in for Lisbie to head home, however in their urgency to take it quickly Cox had remained in an offside position as the Robins were sluggish in getting back to defend.
It was the home side that got back in it a minute later from a corner of their own. Former Orient loanee Scott Wagstaff curled a corner in from the right that was headed down by Aden Flint into the path of Baldock at the back post who pounced to sweep it home.
The goal eased the atmosphere at Ashton Gate and seemed to alleviate some of the pressure on the home side who saw more of the ball in the final third with Marlon Pack going closest after an Emmanuel-Thomas long throw was scrambled away as far as him on the edge of the box.
Against the run of play though it was the O's who re-captured the lead. Moses Odubajo had been quiet by his standards but when James released him in the right channel, the winger unleashed a fierce low volley that Parish fumbled across the face for Cox to bundle in at the back post.
The O's could barely draw breath for the Robins pegged them back once more. Baldock went tearing down the right before beating two O's players and squaring it a dangerous ball across the face that found a way in off of Scott Cuthbert's shins with the defender racing back towards his own goal.
It was harsh on Cuthbert who had been solid throughout but the goal cranked the atmosphere up yet another level to set up a grandstand finish as both sides looked intent on finding a winner though neither could find one as Orient dominated the injury time possession without testing Parish.
ORIENT: Jones, Omozusi, Baudry, Clarke, Cuthbert, Cox, Vincelot, James (Bartley 86), Odubajo, Lisbie (Batt 72), Mooney (Simpson 89)
SUBS: Larkins, Sawyer,Stockley, Wright
GOALS: Mooney (22) Cox (69)
BOOKINGS: Odubajo (86) Bartley (88)
BRISTOL: Parish, Moloney, Williams (Bryan 78), Flint, Baldock, Emmanuel-Thomas, Wagstaff, Cunningham, Pack, Gillet (Elliot 89), Osborne
SUBS: Fielding, Taylor, Shorey, Harewood, McLaughlin
GOALS: Baldock (58) Cuthbert OG (72)
BOOKINGS: Gillett (45) Williams (57)
REFEREE: Andy Davies