United, beaten at Old Trafford in the League Cup by Middlesbrough on Wednesday, played out a goalless stalemate with Manchester City last weekend and failed to find the net once again as Alan Pardew's side held firm on Saturday.
Palace welcomed former United winger Wilfried Zaha back into their starting line-up, but he was outshone by Yannick Bolasie on the opposite flank.
The Democratic Republic of Congo international rattled the crossbar inside 10 minutes as Palace applied the early pressure.
United soon found their feet, but were bereft of ingenuity despite their dominance of possession - a Wayne Rooney free-kick that forced a routine save from Wayne Hennessey was their best effort of the first half.
Yohan Cabaye, recovering from a knock sustained in the 5-1 League Cup thrashing at City in midweek to retain his place in the starting line-up, Scott Dann and Dwight Gayle were all unable to take second-half chances, leaving Palace winless in 13 Premier League clashes with United.
United made two changes in defence with Matteo Darmian replacing the injured Antonio Valencia and Daley Blind coming in for Phil Jones at centre-back.
But Van Gaal's side looked shaky at the back in the opening stages and would have fallen behind in the 10th minute had David de Gea not got the slightest of touches on Bolasie's effort to turn it onto the bar.
De Gea came to United's rescue once more two minutes later, leaping up to palm over a header from Dann following Cabaye's corner.
The visitors eventually took control of possession, but struggled to build anything positive against a robust Palace team.
Hennessey was not tested until the 25th minute, when Rooney fired a 25-yard free-kick over the wall that the Palace goalkeeper was able to get across to and save.
Hennessey thwarted Rooney again six minutes later, exposing the striker's lack of pace by rushing out to stop him from latching onto an incisive pass from Anthony Martial.
There were chances for Gayle and Ander Herrera before the interval, but neither player made strong enough contact with the ball to trouble the opposing.
Goal-scoring opportunities remained at a premium for the two sides during a scrappy start to the second half, with De Gea and Hennessey acting as spectators.
Although Palace grew into the game and controlled the ball, it took them until the 71st minute to carve out a decent opening.
Joel Ward's delivery from the right found Cabaye unmarked 10 yards out, but he was unable to steer his volley on target. Dann looped a header wide before Gayle had a shot saved by De Gea in the 76th minute.
There were chances for both sides to steal all three points late on, but Damien Delaney got a crucial block on a Martial shot before Bolasie headed over from a corner in stoppage time.
