Having dominated the opening half, Simon Weaver's team went 1-0 down within 60 seconds of match restarting, but Dan Jones drew them level just before the hour-mark.
Yet another defensive mistake then gifted the O's a second, and although Jack Muldoon missed a 73rd-minute penalty, Josh McPake came to the Sulphurites' rescue with a richly-deserved equaliser soon afterwards.
Winless in six games prior to kick-off, the hosts began with real intensity and went onto deliver their best 90-minute performance in some time.
Initially their play when they had the ball left a little to be desired, but with Orient struggling to cope with the way they were being pressed all over the park, Town were soon in charge of proceedings.
They should have taken the lead on 20 minutes when Will Smith nodded down George Thomson's right-wing corner and, after a visiting defender failed to deal with the danger, Jon Stead blazed over the cross-bar from just outside the six-yard box.
Less than 60 seconds later Stead pulled the ball back from close to the right-hand byline and O's custodian Lawrence Vigoroux could only push the ball into the path of Lloyd Kerry.
But, with the goal gaping, the stretching midfielder stabbed the ball over the top.
Josh Falkingham then won possession wide on the home right and delivered an inviting low cross which Stead looked set to convert at the far post, only for Sam Ling to nip in with a crucial intervention.
Harrogate continued to turn the screw and Connor Hall dragged a 20-yard strike wide of the mark before Kerry shot straight down the throat of Vigoroux from slightly further out.
The East Londoners began to see a little bit more of the ball as the interval approached and then made the perfect start to the second period.
For the third game in a row, the Sulphurites switched off having come out after half-time and found themselves trailing - against the run of play.
Less than a minute had passed following the resumption when Connor Wilkinson raided down the right and unleashed a low strike that looked to go through the legs of James Belshaw.
In recent weeks, Town's response to suffering set-backs has been poor, but on this occasion they kept their heads up and kept asking questions of their visitors.
And they got their reward on 58 minutes as George Thomson floated over a free-kick from the left and Jones rose inside the six-yard box to nod home, ending his team's six-hour wait for a goal at Wetherby Road.
Weaver's men looked to have the bit between their teeth at this point, but once again conspired to shoot themselves in the foot and gift Orient a second of the evening.
Thomson sliced an attempted clearance inside his own box, and rather than clear the ball, Jones tried a risky header back to Belshaw, which was pounced on and tapped home by the predatory Danny Johnson.
Had Town heads dropped at this point it would have been understandable, but they kept themselves in the contest and were gifted a golden opportunity to bag a second equaliser on 73 minutes.
Muldoon produced a neat turn to get the better of Dan Happe inside the away box and was floored by the big O's centre-half.
Harrogate's 12-goal top-scorer took responsibility for the resulting spot-kick himself, though his poor strike from 12 yards was comfortably pushed away by Vigoroux.
But, Orient couldn't clear their lines from the resulting corner and when the ball was eventually recycled for Hall, he managed to find McPake on the left-hand side of the penalty area.
And the Glasgow Rangers loanee came up with the goods, sparing the blushes of both Jones and Muldoon by sending a low effort across Vigoroux and inside the far corner.
Buoyed by that strike, Harrogate looked the more likely in the closing stages with Thomson, McPake and Kerry all forcing Vigoroux into action, while Orient's Dan Kemp went close with a diving header at the opposite end of the field.
An even better opportunity for the East Londoners to snatch all three points then presented itself in the 89th minute, Belshaw coming to the hosts' rescue with a fine save from Johnson's close-range header.
Stoppage-time saw Muldoon and McPake both get into dangerous areas, though both men continued the theme of placing their strikes too close to Vigoroux and the game ended all-square.
Harrogate Town: Belshaw; Burrell, Smith, Hall, Jones; Thomson, Falkingham, Kerry, McPake; Stead, Muldoon. Unused substitutes: Cracknell, Fallowfield, Kiernan, Francis, Williams, Andrews.
Leyton Orient: Vigoroux; Ling; Akinola, Happe, Brophy, Clay, Kyprianou (Abrahams 87); Wilkinson (Dennis 77), McAnuff (Freeman 71), Kemp; Johnson. Unused substitutes: Sargeant, Widdowson, Coulson, Turley.
Referee: A Backhouse (Carlisle).