The match turned on the introduction of Giroud as a 69th-minute substitute after a Jermain Defoe penalty had equalised Sanchez's first-half opener to give the home side a flicker of hope.
Giroud scored with his opening two touches, first with a superb left-foot shot from a Kieran Gibbs cross on 71 minutes and then with a near-post header from a corner five minutes later.
Sanchez scored Arsenal's third goal in seven minutes from close in when Gibbs's shot came back off the post.
The easy victory was no more than Arsenal deserved after enjoying 66 percent possession and spurning several chances to finish the game.
Asked whether he deserved credit for the decision to bring on Giroud, manager Arsene Wenger said: "The manager gets easy credit when he has quality players on the bench. You do not need to be a special manager to make that decision."
The defeat will place manager David Moyes under further pressure as he seeks to turn round what is now the worst start to a season after 10 games by any side in Premier League history, inferior to Manchester City in 1995-96 on goal difference.
"Were trying (to turn things around)," said Defoe. "It is difficult to stay positive but our position is reality, that's what it is. The important thing is to stick together like we did last year."
(Reporting by Neil Robinson; Editing by Clare Fallon)
