The home side began well and Frazer Richardson forced Clayton Ince into a stretching save with a 30-yard drive and then Nick Bailey headed over soon after from close range.
The Addicks eventually broke through on the half hour, with Llera getting on the end of Bailey's cross to poke home.
Deon Burton had an effort well saved by Ince and Jonjo Shelvey went close with an ambitious long-range effort as they upped the ante.
Charlton were in total control and doubled their lead in the 72nd minute when Deon Burton set up Wagstaff and he produced a neat finish, finding the corner from 12 yards.
Walsall rallied and tried to mount a comeback as Sam Parkin headed a Matt Richards cross against the post. Troy Deeney also wasted a good chance when he headed over from close range.