Defender Mat Baudry proved to be the unlikely goal hero as Orient came back from the dead and grabbed a point with a far-post finish just before the hour after Wolves had made a storming start and taken a fourth-minute lead.
Ethan Ebanks-Landell fired the home side ahead in front of a crowd of almost 29,000 and Wolves threatened to run riot in the first half.
But a patched-up Orient side, who lost Romain Vincelot through injury at the break, dug deep in the second period and showed their battling qualities as Baudry finished off a neat free-kick to earn a point that few of the travelling fans could have envisaged at half-time.
Orient manager Russell Slade was forced into making two changes to the side that had won at Gillingham on Boxing Day.
Robbie Simpson came in for the injured Shaun Batt, while Lloyd James returned following a suspension, but Scott Cuthbert was missing after picking up his fifth booking at the Gills which triggered a one-game ban.
It meant that young keeper Jake Larkins continued in goal for the injured Jamie Jones and there was no return for striker David Mooney, whose three-game suspension had lapsed, but a foot injury kept him side-lined.
In front of a sell-out crowd it was important for the O’s to keep things tight early on and give little away to silence the mass ranks of Wolves fans.
However, the O’s surrendered possession cheaply in the early stages and paid the price on just four minutes when the home side swept into the lead.
Wolves swept the ball to the right and Ebanks-Landell in splendid isolation, cut in and hammered a fierce effort across Larkins and into the net.
O’s were forced to play on the break and did have their moments – but Wolves could have been out of sight by the interval.
The visitors first chance fell to Simpson after Moses Odubajo sent in a cross from the right and the striker’s back-header drifted just over the bar.
But most of the action was at the other end as the pace of Michael Jacobs was causing Orient all sorts of problems and when visiting skipper Nathan Clarke conceded possession with a tame header Jacobs raced clear, but Larkins blocked his effort.
Kevin Lisbie tried manfully to work his magic up front and sent in a teasing cross that home keeper Carl Ikeme held, before Jacobs caused problems again with a rampaging run and cross down the left.
Clarke then atoned with a wonderful life-saving tackle to deny Jacobs after he burst through the visiting defence and looked odds on to score.
Jake Cassidy was then left shaking his head in disbelief as Larkins did well to parry a shot from Jacobs and he screwed the rebound wide of the post with the goal gaping.
The energetic Romain Vincelot came close to a leveller when he headed a James corner over – but the half-time whistle must have been music to the ears of the visitors as they headed to the sanctuary of the changing room just one goal adrift.
The O’s were forced into a change at the break as Vincelot had picked up a knock just before the interval and he was replaced by Gary Sawyer at the start of the second half which necessitated a defensive reshuffle, while Wolves also made a change with Dave Edwards replacing Jack Price.
Orient made a better start to the second half, but were almost caught out on the break as Kevin McDonald raced clear following an O’s corner, but Larkins made a fine save and recovered to clear the danger as James Henry was about to slide the ball into an empty net.
But as Orient started to get a foothold in the game the home side looked increasingly anxious and the visitors levelled on 59 minutes when a quickly-taken free-kick ended with Odubajo whipping in a cross from the right and Baudry arrived at the far post to fire home from close range.
Orient dug in and when Yohann Lasimant replaced Simpson his pace started to worry the home side and O’s almost went in front went in front on 80 minutes when Lisbie led a raid down the left and cut the ball back for the French striker to fire inches over the top from 20 yards.
The expected Wolves late onslaught failed to materialise and if any side were likely to snatch a winner in the dying seconds it was Orient, who showed true grit and determination to come back from the dead and earn another important away point.
Wolves: Ikeme, Stearman, Batth, Henry (Griffiths 70), Sako, McDonald, Cassidy (Doyle 84), Ricketts, Price (Edwards 46), Ebanks-Landell, Jacobs.
Subs not used: Hennessey, Evans, Golbourne, Bancessi.
Wolves goals: Ebanks-Landell (4)
Wolves bookings: Cassidy (73 unsporting behaviour)
Leyton Orient: Larkins, Omozusi, Vincelot (Sawyer 46), Baudry, Cox, James, Lisbie, Odubajo, Clarke, Bartley, Simpson (Lasimant 70)
Subs not used: Lee, Gorman, Finney, Ling, Grainger.
Orient goals: Baudry (59)
Orient bookings: James (23 foul), Vincelot (39 foul), Baudry (66)
Referee: David Coote