Unfortunate second-half own goals from Kory Roberts and Liam Kinsella condemned the Saddlers to defeat at play-off chasing Charlton.
The first real opportunity of the game fell to Charlton on 25 minutes, Josh Magennis getting away from Kory Roberts but his low right-footed drive was tipped wide by keeper Liam Roberts.
The Addicks went ahead on the half-hour as Mark Marshall’s inviting left-wing cross was side-footed home on the volley by Joe Aribo.
With their tails up, Charlton could have made it 2-0 when Stephy Mavididi thundered a blistering 20-yard drive against the bar.
The Saddlers grew stronger as an attacking force in the final ten minutes of the half.
Addicks keeper Ben Amos beat away Tyler Roberts’ left-footed shot and Oztumer exchanged passes with the West Brom loanee before lashing wide of the near post.
An equaliser duly arrived on the stroke of half-time, Luke Leahy delivering a pinpoint cross for Oztumer to glance a fine header in off the far post.
A sweet moment for the diminutive playmaker, who was released by the London club as a youngster for being too small.
The visitors should have taken the lead almost straight after the restart.
Joe Edwards dispossessed Harry Lennon and squared towards Amadou Bakayoko, who would have had a tap-in, but a Charlton man nipped in to intercept.
The ball came back to Edwards, who skipped past his marker before rifling a powerful strike against the underside of the bar.
Back came Charlton, with Aribo playing Magennis through on goal but he fired straight at Liam Roberts.
Tariqe Fosu came on for the hosts after 51 minutes and was immediately in the thick of the action, seeing two near-post efforts parried by Liam Roberts in quick succession.
Walsall were looking threatening too, with Leahy seeing a flicked front-post header from Oztumer’s in-swinging corner clawed out by Amos.
The Saddlers had a better chance moments later as Tyler Roberts displayed superb skill before slipping in Bakayoko, whose low strike was kept out by the legs of Amos.
Karl Robinson’s side hit back, Magennis heading against the post from Marshall’s corner and Fosu blazing the rebound over.
Charlton could gone in front moments later but Liam Roberts produced a fantastic one-handed save to tip away Aribo’s header from Fosu’s free-kick, with Leahy blocking Lennon’s follow-up on the line.
The pressure paid off on 73 minutes as Kory Roberts, attempting to dispossess Mavididi when clean through, inadvertently poked the ball past his own keeper to put the Addicks ahead.
Marshall could have extended Charlton’s lead ten minutes later but he fired wastefully over from Fosu’s accurate pull-back.
The Saddlers had a wonderful chance to level three minutes from time.
Bakayoko and Tyler Roberts combined smartly but the latter’s cut-back towards Oztumer, completely unmarked in the centre of goal, was way over-hit.
And the home side put the result beyond doubt moments later, with a goal very similar to their second.
Mavididi cut inside from the left and, as he looked to pull the trigger, Liam Kinsella this time prodded past Liam Roberts and into the corner of the net.
Team: L Roberts, Kinsella, K Roberts, Guthrie, Leahy, Chambers, Edwards, Oztumer, Devlin, T Roberts, Bakayoko.
Subs not used: Gillespie, Devlin, Flanagan, Shorrock, Kouhyar, Jackson, Candlin.
Attendance: 10,410 (295 Walsall supporters).