Saville struck after 50 seconds to settle things at the Riverside and ensure Jonathan Woodgate won his dug-out duel with former Leeds team-mate Lee Bowyer and celebrate back-to-back home wins for the first time in his managerial career.
Middlesbrough were without nine senior players through a combination of injury, illness and suspension, meaning Woodgate had to hand 19-year-old Djed Spence a first league start.
But his patched-up side did him proud as they claimed a fourth win of the season.
The Teessiders had been thrashed by Leeds in their previous game but any fears of an Elland Road hangover were dispelled as they claimed the lead inside a minute.
Ashley Fletcher nipped in ahead of Dillon Phillips to prevent the Charlton goalkeeper from gathering Britt Assombalonga's deflected shot and the ball broke kindly for Saville, who swept home his first goal of the season from inside the area.
It came at the start of a first half that was completely dominated by the hosts, who caused a series of problems down the flanks thanks to direct running of Spence and fellow youngster Hayden Coulson.
Saville curled a sixth-minute strike wide as Boro controlled the early stages and Coulson went close midway through the first half when he cut in from the left, only for his side-footed shot to be blocked.
The chances continued to come before the break but Boro's forwards were unable to make the most of them.
Assombalonga fired over on the half-hour mark after his initial shot had been blocked by Deji Oshilaja and glanced a header wide after Adam Clayton floated over an inviting cross from the right.
Charlton failed to record a single effort at goal before the interval, forcing Bowyer into a double half-time change that saw Lyle Taylor return to the fray after an injury absence that had sidelined him since the end of August.
The visitors were a livelier proposition in the second half, although Boro still came close to claiming a second goal as Assombalonga met Coulson's cross with a back-post header that was saved by Phillips.
Marcus Tavernier wasted an excellent opportunity as he volleyed Spence's cross over the bar from the edge of the six-yard box before Charlton finally recorded their first shot with 20 minutes left, Conor Gallagher curling just past the far post after cutting in from the left.
With the Addicks finally coming to life, Boro were hanging on in the closing stages and Aynsley Pears made a crucial save with one minute left, flinging himself to his right to keep out Albie Morgan's low drive.