Arsenal were without Pierre-Emerick Aubameyang, Emile Smith Rowe and Martin Odegaard, while John Egan, Ethan Ampadu and Oliver Burke returned to the United starting line up.
The Gunners came close in the opening minute of the game. Gabriel Martinelli fed Bukayo Saka on hs left and he smashed a powerful strike towards the near post but it it flew narrowly over the crossbar.
The Blades responded with ten minutes gone. Ben Osborn found David McGoldrick and his effort towards the bottom right corner went just wide.
Mikel Arteta's side then broke on the counter-attack in the 24th minute. Lacazette laid it wide to Martinelli down the left and he surged into the box but his shot hit the side-netting.
Arsenal opened the scoring after 33 minutes with a goal of real beauty. Some lovely one-touch football around the edge of the penalty area involved Bukayo Saka, Thomas Partey and Dani Ceballos, whose deft backheel flick eventually put Alexandre Lacazette through on goal to slide the ball beneath Aaron Ramsdale.
Shortly before half-time, Oliver Norwood crossed into the box and it was cleared straight to Egan, who volleyed at goal from a tight angle but Bernd Leno made a good save.
Gabriel Martinelli doubled Arsenal's lead midway through the second half, reacting quickest to tap the ball into an empty net after Ramsdale had parried Nicolas Pepe's shot.
It was 3-0 in the 85th minute. Thomas Partey released Lacazette with a defence-splitting ball and he coolly slid it into the bottom left corner of the net to cap off a convincing win for the visitors.