Solskjaer’s men were abject throughout, playing without rhythm or fluidity.
At half-time, they found themselves behind, thanks to Andros Townsend coming close and having created few opportunities.
Zaha rightly doubled the advantage midway through the second half, scoring on the spot after VAR intervened.
First, Martin Atkinson allowed a handball penalty against Victor Lindelof after seeing a monitor, but when David de Gea turned down Jordan Ayew the Spaniard was penalized for encroachment and Zaha made no mistakes.
Donny van de Beek came off the bench to score in his debut, but Zaha managed all three points with a late clinical finish after proving too strong for Lindelof.
Hodgson’s men drop to six points from their first two games, but United will have to do much, much better in their attempt to get closer to Liverpool and Manchester City.
A new central defender could help.
Here are five talking points from Old Trafford …
Dan James struggles continue
The Welshman received a surprise start wide on the right, with Mason Greenwood only on the substitutes bench.
But James, who after an initially brilliant start looked somewhat intimidated towards the end of last season, had little impact.
His struggles to play in small pockets see him looking to stay on the sideline – especially on the right flank.
And young full-back Tyreek Mitchell was at ease throughout their first half game.
An opportunity not seized.
United midfielder’s balance
The only thing that was really impressive about United after Project Restart was the relationship formed between Bruno Fernandes and Paul Pogba.
When United were hot, this duo, playing side by side, were wonderful and had a clear appreciation for each other.
But they didn’t pick up where they left off against Palace.
Pogba, associated with Scott McTominay, was too deep to really influence the game, and the distance between him and the Portuguese was just too great to dominate Palace. There weren’t enough times they were able to connect, and almost none in the final third.
Maybe Pogba, after only a week back in training, wasn’t as fit as his manager thought he was? It may well have played a role.
Solskjaer needs to find the right balance in midfield, but it wasn’t quite that.
A nightmare for United’s defense
If Victor Lindelof and Harry Maguire are to be Solskjaer’s premier couple and stay there, they need to improve quickly.
Because it was horrible. Absolutely awful. At a time.
Forget the penalty given against Lindelof. Disregard this.
The rest of the game the pair were everywhere.
Positioning was disastrous at different times of the two – Maguire was lazy in not covering the space on the first base – they battled for speed against Jordan Ayew and Zaha, but continued to race with the two. first of the Palace.
Their faint from the back was largely sloppy, and neither was particularly commanding in the air or in the tackle – witness Lindelof on third base.
United have every right to expect better.
Zaha makes her mark
Wilfried Zaha has only made four appearances for Manchester United and failed to make his mark at Old Trafford.
Upon his return this time around, he both took the lead and wore the captain’s armband for the Eagles.
And he duly achieved a winning performance.
His penalty was taken with aplomb, his second shot hard and low and into the bottom corner, but more than his goals he was exceptional.
Unrestrained on the left side, he worked all the way down the line, used his skill and speed to terrorize the United defense, but also showed intelligence in bringing others into play and strength in holding the ball and get his team on the field.
A great all-rounder.
Manchester United are looking to forge their way to the top. Ole Gunnar Solskjaer has already brought in Donny van de Beek but Jadon Sancho remains Manchester United’s number one target.
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Martin Atkinson’s decision to handball a handball penalty against Lindelof was bad enough.
The decision after De Gea refused Ayew to order a restart, for encroaching on the goalkeeper, whom Zaha had scored, was perhaps worse.
“It’s an absolute disgrace,” Gary Neville said. “We’re talking millimeters. It’s incredible. “