The visitors had taken a first-half lead through Harrison Dunk and looked set to add to their five successive League Two wins until Palmer's late intervention.
There was little between the two teams in the opening 20 minutes, although the visitors' Luke Berry saw his ninth-minute cross-cum-shot go across the face of the goal with nobody on hand to apply the final touch before the ball ran narrowly wide of the far post.
The deadlock was broken on 21 minutes when full-back Myles Judd blocked a Berry shot in the penalty area and the ball fell to the unmarked Dunk, who had the simplest of chances to tuck the ball into the net.
From that point on the well-organised visitors were seldom asked any serious questions by their lacklustre hosts.
Uche Ikpeazu almost doubled the visitors advantage when his effort brought a good save from home keeper Alex Cisak. The O's shot-stopper was also called into action diving at full stretch to keep out a firm drive by substitute Max Clark.
But Palmer was to have the last word as Cambridge failed to clear the danger and Michael Collins played in the striker, whose shot took a deflection before squeezing under U's keeper Will Norris to give the hosts an unlikely point.
Report supplied by the Press Association.
Match ends, Leyton Orient 1, Cambridge United 1.
Second Half ends, Leyton Orient 1, Cambridge United 1.
Foul by Josh Koroma (Leyton Orient).
Luke Berry (Cambridge United) wins a free kick in the defensive half.
Substitution, Cambridge United. Joe Pigott replaces Uche Ikpeazu.
Goal!  Leyton Orient 1, Cambridge United 1. Ollie Palmer (Leyton Orient) left footed shot from the centre of the box to the centre of the goal. Assisted by Paul McCallum.
Michael Collins (Leyton Orient) wins a free kick in the attacking half.
Foul by Uche Ikpeazu (Cambridge United).
Substitution, Cambridge United. Ben Williamson replaces Harrison Dunk.
Corner,  Cambridge United. Conceded by Alex Cisak.
Paul McCallum (Leyton Orient) is shown the yellow card for a bad foul.
Foul by Paul McCallum (Leyton Orient).
Leon Legge (Cambridge United) wins a free kick on the left wing.
Corner,  Cambridge United. Conceded by Tom Parkes.
Attempt missed. Josh Koroma (Leyton Orient) right footed shot from outside the box is close, but misses to the left.
Corner,  Cambridge United. Conceded by Gavin Massey.
Attempt missed. Gavin Massey (Leyton Orient) left footed shot from outside the box misses to the left.
Corner,  Leyton Orient. Conceded by Mark Roberts.
Attempt blocked. Paul McCallum (Leyton Orient) header from very close range is blocked.
Josh Koroma (Leyton Orient) wins a free kick in the defensive half.
Foul by Brad Halliday (Cambridge United).
Brad Halliday (Cambridge United) is shown the yellow card for a bad foul.
Myles Judd (Leyton Orient) is shown the yellow card for a bad foul.
Foul by Myles Judd (Leyton Orient).
Harrison Dunk (Cambridge United) wins a free kick in the defensive half.
Harrison Dunk (Cambridge United) hits the bar with a header from the centre of the box.
Foul by Ollie Palmer (Leyton Orient).
Mark Roberts (Cambridge United) wins a free kick in the attacking half.
Attempt saved. Uche Ikpeazu (Cambridge United) right footed shot from outside the box is saved in the centre of the goal.
Substitution, Leyton Orient. Josh Koroma replaces Sandro Semedo because of an injury.
Corner,  Cambridge United. Conceded by Alex Cisak.
Attempt saved. Max Clark (Cambridge United) right footed shot from outside the box is saved in the bottom left corner.
Attempt blocked. Luke Berry (Cambridge United) left footed shot from the centre of the box is blocked.
Substitution, Cambridge United. Max Clark replaces Conor Newton.
Foul by Nicky Hunt (Leyton Orient).
Brad Halliday (Cambridge United) wins a free kick in the defensive half.
Corner,  Leyton Orient. Conceded by Leon Legge.
Attempt blocked. Ollie Palmer (Leyton Orient) right footed shot from outside the box is blocked.
Corner,  Leyton Orient. Conceded by Greg Taylor.
Ollie Palmer (Leyton Orient) wins a free kick in the defensive half.
Substitute Ollie Palmer salvaged a point for Leyton Orient in stoppage time as they drew with Cambridge United at Brisbane Road.