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Dover continued their excellent home run by taking a point off the National League leaders on Saturday.
The draw made it five unbeaten in the league at Crabble and Whites might have secured a fifth successive home win had top scorer Inih Effiong not seen an early penalty saved by visiting keeper Dean Brill.
Alfie Pavey was also unlucky with a fierce drive which smacked against the crossbar in the opening seconds of the second half.
Boss Andy Hessenthaler was forced into three changes with Josh Passley, Bobby Joe Taylor and Ricky Modeste all out after picking up injuries in the Boxing Day win over Maidstone.
In came Josh Debayo, and, for their first league starts, centre-half Scott Doe, and forward Alfie Pavey. Midfielder Nortei Nortey was recalled to the starting line-up with winger Anthony Jeffrey dropping to the bench.
The visitors boast the division's best away record and made a lively start but from Dover's first incursion into the Os box, after six minutes, Effiong was sent sprawling by keeper Dean Brill to earn a penalty.
Effiong had missed from the spot in Dover's opening league game against Wrexham, and he again lacked conviction as his poorly struck effort was parried away to his left by Brill.
From the corner Pavey saw his firm header pushed away by Brill with Kevin Lokko then directing the rebound over the bar.
The game had a real cut and thrust feel to it after that with Orient looking quick on the counter but they created little.
Dale Gorman fired wide in the opening seconds but otherwise Mitch Walker was not really extended, claiming a number of corners with relative ease.
There was a dangerous moment just before the half-hour when Matt Harrold's flick sent Josh Koroma clear but with the division's top scorer Macauley Bonne in support his first touch was poor and Doe got across well to clear.
Nortey then fired over after a cute pass from Jai Reason but moments after the Os should have been in front when Koroma broke clear only to fire over from 12 yards.
Koroma was the guilty man again on 38 minutes when Bonne played him in behind the home defence but as Walker came out the winger lifted his shot over the keeper and wide of the far post.
Whites would have been happy with the way the first half went and they almost made a dream start to the second when Pavey thundered a shot against the crossbar with Brill beaten.
Brundle then fired well over after being well picked out by Nortey and Pavey had another effort wide after good play in the build-up by Effiong.
Whites looked the more likely winners at this stage with Orient only venturing forward sporadically.They sent a few crosses into the box but Walker's handling was faultless.
Koroma, such a threat before the break, was more subdued in the second half but did force Walker into a low save on 77 minutes.
Gorman then wasted their best chance of the second half two minutes later when he tried to beat Walker at his near post but fired wide.
The same player then curled an effort wide before Walker's hacked clearance almost put Effiong in at the other end. The big striker got a foot to Joe Widdowson's poor back header but the ball rolled wide.
There was one last scare for Whites on 89 minutes when Gorman's low drive smacked against the foot of the post but there was no denying the home side deserved their point, making it 14 from the last 21. They remain 20th with 25 points from 27 matches.
Dover: Walker, Brundle, Doe, Lokko, Debayo, Gomis, Lewis, Nortey (Jeffrey 72mins), Reason, Effiong, Pavey; Subs: Worgan, Diarra, Bedford, Allen.
Leyton Orient: Brill, Widdowson, Ling, Coulson, Ekpiteta, Koroma, Gorman, Brophy (Lawless 62mins), Lee, Harrold (Alabi 79mins), Bonne; Subs: Sargeant, Happe, Sotiriou.
Attendance: 2,270 (755 Orient fans).