The Red Devils, who were watched by new boss Erik Ten Hag in south London, were able to at least avoid the embarrassment of lining up in the Europa Conference League next season due to West Ham losing away to Brighton.
It meant United clinched sixth after this 1-0 defeat but they finished on 58 points – the lowest they have ever accumulated in the Premier League – in a campaign which showed how far they are behind Manchester City and Liverpool, who were involved in a dramatic final day that saw the title again lifted at the Etihad Stadium.
One of Ralf Rangnick’s final acts in charge was to hand Hannibal Mejbri a first league start and there were several other youngsters on the bench at Selhurst Park, including Robbie Savage’s son Charlie.
Patrick Vieira also shuffled his pack and teenager Jesurun Rak-Sakyi was given his full debut for Palace, who had endured a difficult night at Goodison Park on Thursday where they let slip a two-goal lead and saw their manager involved in an altercation with a fan after full time.
It was United who started the better of the two sides with a Bruno Fernandes effort blocked by Conor Gallagher before Edinson Cavani’s scuffed shot was parried away by a wrong-footed Vicente Guaita minutes later.
The visitors knew victory in front of incoming boss Ten Hag would guarantee a place in the Europa League next season and the deadlock should have been broken in the 25th minute when Cavani sent Anthony Elanga away but he dragged wide from inside the penalty area.
Palace were jolted into life after that opportunity with the hosts squandering two openings over their own soon after.
First David De Dea denied Zaha’s left-footed strike before Jeffrey Schlupp fired straight at the Spanish goalkeeper following a superb Odsonne Edouard flick.
The opener did arrive with eight minutes of the first half left and it was ex-United man Zaha who provided it but only after a big helping hand from Fernandes.
Fernandes kicked Alex Telles’ throw back towards his own goal and Zaha latched onto the loose ball, created space away from Diogo Dalot and Victor Lindelof before he rifled into the bottom corner for his 15th goal of the season.
United improved after the break and it was former Monaco attacker Mejbri who did his utmost to get the visitors back on level terms.
Fine defending by Joel Ward denied the teenager after he had raced into the area before his curling shot was tipped over by Guaita.
It was somewhat of a surprise to see Rangnick withdraw Mejbri just past the hour mark and by this point it could have been 2-0 had Conor Gallagher – on the final appearance of his season-long loan – angled his shot inside the post from 20 yards.
More Under-23s were thrown on by Rangnick with Shola Shoretire and Alejandro Garnacho introduced but the latter could not get on the end of Fernandes’ cross late on.
The final chance fell to Scott McTominay in stoppage time but he blazed wide to highlight the size of the task for Ten Hag, who officially starts on Monday while Palace conclude an excellent first season under Vieira in 12th.