Dunk managed to slot home from six yards out after the ball fell kindly to him in the box, and the O’s left it extremely late to pick up a point as Palmer’s deflected effort trickled past Will Norris to ensure the O’s made it three games unbeaten at home going into the new year.
The O’s kept faith with the same starting XI which won 3-2 against Crawley Town on Boxing Day, with the only change seeing Jay Simpson left out of the squad and Callum Kennedy returning to the bench after missing the Crawley game with a groin injury.
Unlike Boxing Day, chances were few and far between in the early stages. The closest either game in the opening 10 minutes was when Paul McCallum got his head to Michael Collins’ free-kick, but it was comfortable for Will Norris to hold in the U’s goal.
Cambridge and Luke Berry went even closer as his teasing cross was just missed by Uche Ikpeazu in the box and the cross just curled wide of Alex Cisak’s far post.
Nicky Hunt isn’t known for his goalscoring prowess but almost doubled his season’s tally as the ball feel to him invitingly 30 yards from goal and his right-footed shot was inches wide of the post.
However, parity didn’t last for much longer though as after Myles Judd denied Luke Berry, the ball fell kindly to Harrison Dunk who slotted past Cisak to break the deadlock on 21 minutes.
As O’s went in search of a reply, Mark Roberts did well to clear Tom Parkes’ header back across goal behind for a corner, before Cisak saved comfortably from a Berry effort from just outside the box.
Teddy Mezague’s game was over though on 33 minutes when he pulled up with what looked like a groin injury, and was replaced by Yvan Erichot.
Chances were limited as the half wore on, though Collins did well to head behind another dangerous Berry delivery as the visitors took a 1-0 lead into half time.
No changes were made at the break by either side, and it was the O’s who created the first chance of the half when Judd and Massey combined well down the right.
The former dinked a ball over Greg Taylor for the winger who put a ball into the box, though no-one was able to challenge as Norris comfortably picked up the loose ball.
Another change was forced upon the O’s seven minutes into the second half with Sam Dalby forced off through an ankle injury, and was replaced by Ollie Palmer.
The O’s were almost undone on the break from a corner as the ball found its way to Ikpeazu and he found a way into the box but saw his shot held by Cisak.
An inswinging delivery from Semedo saw the U’s put the ball behind for another corner and from that set piece, McCallum got a header in on goal but Norris got down well to keep the effort out.
That had given the O’s a visible left and Palmer saw a shot deflected behind for a third corner in quick succession, though unfortunately it came to nothing.
Ikpeazu thought he had extended the visitors advantage just after the hour mark when the ball deflected into the path of the striker and he flicked it home, only for the offside flag to be raised.
Cambridge continued in their search for the second and it almost came from Berry, only for Atangana to make a last-ditch block, before Cisak was forced to push an effort from Piero Mingoia wide of the post.
Dunk could well have doubled his and the U’s tally for the afternoon when getting on the end of a teasing delivery from Brad Halliday but his header from an acute angle struck the top of the bar and over.
Norris was called into action up the other end when he managed to get the slightest touches on McCallum’s header from a Collins free-kick as the O’s continued to push, but couldn’t find much in terms of chances.
As the game entered the final 10 minutes Josh Koroma dragged an effort wide, before Palmer’s weak effort was held by Norris.
Parkes blocked an Ikpeazu strike up the other end as time began to tick away and though Orient had plenty of the ball, there were very few chances created in the closing stages, until the 95th minute.
And that was when the O’s levelled as the ball fell to Palmer inside the box and the strike deflected past a helpless Norris to secure a share of the spoils for Andy Edwards’ side ahead of their trip to Exeter City on Monday.
ORIENT: Cisak, Judd, Parkes, Mezague (Erichot 33), Hunt (c), Massey, Atangana, Collins, Semedo (Koroma 67), Dalby (Palmer 53), McCallum.
SUBS: Sargeant, Kennedy, Weir, Bowery.
GOALS: Palmer (90+5)
BOOKED: Judd (68), McCallum (83)
CAMBRIDGE: Norris, Halliday, Roberts, Legge, Taylor, Newton (Clark 62), Dunne, Mingoia, Berry, Dunk (Williamson 87), Ikpeazu (Pigott 90+5)
SUBS: Gregory, Adams, Long, Dallison, Pigott.
GOALS: Dunk (21)
BOOKED: Halliday (71)
REFEREE: Lee Swabey
ATTENDANCE: 5,897 (1,391 Cambridge United fans)