Two goals in three second half minutes condemned much changed United to a first league defeat since October.
The result kept Arsenal's faint top four hopes alive and left the rotated Reds with eyes and minds on the looming semi final second leg with Celta Vigo.
Paul Pogba, Marcus Rashford, Eric Bailly and Daley Blind were all left on the bench ahead of that match on Thursday, with a Premier League debut for 19-year-old defender Axel Tuanzebe.
He performed admirably too, and fellow Academy graduate Scott McTominay also made his senior United bow as a late substitute.
Granit Xhaka's heavily deflected effort put the Gunners ahead before Danny Welbeck thumped home a header for his third goal in four games against his old club.
United's unbeaten league run spanned 25 games but included several infuriating draws and a resultant failure to make up any significant ground on the sides above them.
The match started at a frenetic pace with chances for both sides inside the opening 15 minutes.
Wayne Rooney headed over from Juan Mata's cross and David de Gea saved superbly to keep out a low Aaron Ramsey effort at the other end.
Phil Jones thwarted Welbeck with a superb lunging block on the half hour mark, and the Gunners went close again moments later as the hosts starts to turn the screw.
Alex Oxlade - Chamberlain collected the ball 25 yards out, and rifled in a deflected effort which de Gea did well to push around the post.
United looked dangerous on the counter attack and could - probably should - have gone ahead just before the interval.
Rob Holding's underhit backless put Rooney through but, with Mata unmarked in the middle, he hesitated and Petr Cech smothered.
Arsenal went ahead on 54 minutes when Xhaka's effort from distance struck Herrera and looped over the stranded de Gea.
With United still reeling, Oxlade - Chamberlain's pinpoint pass picked out Welbeck who rose above Chris Smalling and powered home a header.
Rooney lashed an effort wide before substitute McTominay almost made a dream impact with a 20-yarder but Cech saved well.
Alexis Sanchez fired wide on the angle but Arsenal held firm to leave United fully focused on Thursday's semi final showdown at Old Trafford.
Overall team performance: 5.5/10
United Faithful Man of the Match: Axel Tuanzebe. The only positive.