Comfortably beaten in the Manchester derby a fortnight ago, Jose Mourinho's men - now some 14 points adrift of leaders City - offered only a limp response as the Eagles secured their first point in 12 league visits to Old Trafford.
Roy Hodgson will feel his side should have taken more from the contest with Patrick van Aanholt and Andros Townsend culpable for poor misses either side of half-time.
But having avoided a third successive defeat, the visitors will be satisfied with having added to the pressure that continues to hang over Mourinho.
Though on top early, United were fortunate not to fall behind in the 25th minute as an unmarked Van Aanholt scuffed wide on the end of a counter-attack.
Chris Smalling next nodded past the far post from a Juan Mata free-kick, before Jesse Lingard and Anthony Martial drew close-range saves from Wayne Hennessey.
Palace had the ball in the net moments before half-time, but Cheikhou Kouyate was adjudged to have strayed marginally offside in contesting the header with Victor Lindelof.
The visitors were more thankful to see the assistant's flag raised 10 minutes after the interval as a tight call disallowed Romelu Lukaku's follow-up finish to Ashley Young's initial effort.
Mourinho turned to Marouane Fellaini for impact and the midfielder's first act was to escape without caution for an ugly follow-through on Luka Milivojevic.
United were increasingly vulnerable and were given another reprieve when Townsend screwed his shot across the face of goal after squirming through a pair of challenges, before Hennessey's smart save from a Lukaku header at the other end ensured the points were fittingly shared.
What does it mean? Mourinho still searching for attacking mix
Lukaku's recall at the expense of Marcus Rashford could prove short-lived after United's forward line misfired during a winnable match that left Mourinho with more questions than answers as to his best attacking combination.
Zaha adds zest for plucky Palace
Though he was unable to mark his recovery from a hamstring injury with a goal, ex-Red Devils winger Wilfried Zaha still enjoyed the return to Old Trafford, posing plenty of problems to the hosts' defence and keeping Palace on the front foot.
Martial lets standard slip
Ruled out of the France squad by an adductor issue, the break evidently did little good for Martial as the in-form forward of recent weeks made way for a man unsure of his first touch and unable to make the most of his opportunities.
Key Opta Facts
- United are unbeaten in their last 21 league meetings with Palace (W17 D4).
- This was United's 65th 0-0 draw in the Premier League – 31% of them have come in the six seasons since Sir Alex Ferguson retired (20/65).
- Palace had 13 shots in this match, their most in an away Premier League game this season. However, just two of these were on target.