Arsenal were rewarded for their blistering early pace as Tavares tapped home in the third minute after United goalkeeper David de Gea pushed away a curling effort by Saka, following some poor defending by the visitors at The Emirates.
Saka doubled the Gunners' lead from the penalty spot after a foul on the winger in the build-up to a strike by Eddie Nketiah that went in but was ruled out as offside by the Video Assistant Referee (VAR).
United's sluggish display overshadowed fleeting moments in which they threatened and was another reminder of the challenge facing incoming manager Erik ten Hag, though the visitors got one back as Cristiano Ronaldo swept in Nemanja Matic's cross.
The Portuguese forward's 100th Premier League goal came after a traumatic week personally after the death of one of his newborn twin babies. In a show of support,
Arsenal fans gave the United No 7 a long round of applause in the seventh minute, as Liverpool fans had done in their midweek fixture which Liverpool won 4-0.
United improved in the second half but their woes deepened as skipper Bruno Fernandes hit the post with a poor effort from the penalty spot following Tavares' handball, before a 70th-minute thunderbolt from Xhaka sealed the win for the Gunners.
That came after a brilliant save by Arsenal goalkeeper Aaron Ramsdale to push Diogo Dalot's shot onto the post - the second time in the game the player hit the woodwork, on a frustrating day for United, who also had a Ronaldo strike ruled out for offside.
The win lifted Arsenal to fourth place on 60 points, three ahead of fifth-placed Tottenham Hotspur who take on Brentford later on Saturday. United are sixth, with interim boss Ralf Rangnick facing a tough task in his final four games.