Nuno Tavares opened the scoring early on, before Bukayo Saka doubled the Gunners' advantage, from the penalty spot, after 30 minutes.
United then responded, just minutes later, through Cristiano Ronaldo's 100th Premier League goal, but Bruno Fernandes hit a post with a penalty before Granit Xhaka's long-range effort in the second half ensured it was Mikel Arteta's men who were left the happier of the two sides.
The result leaves the Reds sixth in the Premier League table, and we return to action against Thomas Tuchel's Chelsea on Thursday evening at Old Trafford.
FIRST HALF - GUNNERS AHEAD AS REDS RESPOND
After just a mere two minutes of proceedings at the Emirates Stadium, Arsenal took the lead through full-back Tavares.