The news before kick off was that Erik ten Hag opted to drop Marcus Rashford from the starting lineup because of the busy schedule.
The players that were selected made a fast start to proceedings, with Alejandro Garnacho and Matthijs de Ligt drawing two impressive stops from Henderson.
Man United continued to put their hosts under pressure as Garnacho struck the crossbar before Bruno Fernandes fired the rebound against the woodwork.
Henderson was then required to dive at full stretch to prevent Joshua Zirkzee from turning the ball home from Fernandes's low cross.
For all of Man United's dominance in the first period, Eberechi Eze had the chance to score against the run of play in the closing stages of the first period, but he could only fire straight at the grateful Onana.
While that may have been a comfortable save, there was nothing routine about the superb double save he pulled off in the second period to deny Eddie Nketiah and Ismaila Sarr.
Eberechi Eze then spurned a glorious chance, linking up with Sarr before sending a gilt-edged opportunity just wide of Onana's goal.
Palace were unable to snatch maximum points, but they would have been satisfied to avoid defeat in a fifth consecutive home game against Man United.
The Eagles will finish the day in 16th position, while the Red Devils are in 11th spot after winning two, drawing one and losing two of their five league games.
CRYSTAL PALACE VS. MAN UNITED HIGHLIGHTS
Garnacho and Fernandes rattle the woodwork vs. Crystal Palace (27th min, Crystal Palace 0-0 Man United)
Man United go agonisingly close to breaking the deadlock. Garnacho latches onto Diogo Dalot's defence-splitting pass before sending his first-time strike crashing against the woodwork. The rebound drops to Fernandes, who sends his strike into the ground and off the crossbar.
Onana's double save vs. Crystal Palace (65th min, Crystal Palace 0-0 Man United)
Onana showcases his quick reflexes to stop Palace from taking the lead. The goalkeeper gets down low to keep out Nketiah's driven strike before jumping straight up to throw himself in front of Sarr's follow-up effort.
MAN OF THE MATCH - DEAN HENDERSON
Henderson produced an impressive display against his former club, playing a key part in Palace's efforts to clinch a precious point.
The 27-year-old made seven saves throughout the contest, including numerous stops in the first half to thwart the likes of Garnacho, De Ligt and Zirkzee.
While Henderson was undoubted Man of the Match, Onana may have produced the moment of the contest when he pulled off a superb double save in the second period.
CRYSTAL PALACE VS. MAN UNITED MATCH STATS
Possession: Crystal Palace 33%-67% Man United
Shots: Crystal Palace 9-15 Man United
Shots on target: Crystal Palace 4-6 Man United
Corners: Crystal Palace 4-11 Man United
Fouls: Crystal Palace 7-12 Man United
BEST STATS
WHAT NEXT?
After being held to a point, Man United will attempt to return to winning ways in Wednesday's Europa League clash with Twente at Old Trafford.
As for the Eagles, they hope to clinch their first Premier League win of the season when they travel to Goodison Park for a meeting with Everton next weekend.