The Egyptian Gedo, a deadline-day addition for the Tigers, scored as a substitute against Derby last time out and hit the target again on his full debut.
The 33rd-minute winner was hardly a collector's item, a scrambled close-range finish from a corner, but Hull were good value for three points in a match they largely dominated.
The promotion-chasers came out aggressively, with Gedo's compatriot Ahmed Elmohamady the favoured outlet on the right wing. He got to the byline in the third minute before cutting the ball across the six-yard box, where Michael Morrison got just enough on it to deflect it away from danger.
Hull were inches away from the opener after seven minutes, Paul McShane's cross finding David Meyler whose header was cleared off the line by Dale Stephens with keeper Ben Hamer beaten.
Charlton began to settle and in the 20th minute Johnnie Jackson made a strong run towards the final third only to see his cross intercepted by Robbie Brady.
But it was the hosts who took the lead in the 33rd minute after Gedo's perseverance won a corner from the right.
Brady delivered it, Hamer missed his punch and Gedo was on hand to bundle home at the back post.
Just a minute had passed in the second half when Hull went close to extending their lead. A Brady corner was again the cause but McShane produced an air-kick with the goal gaping.
Charlton hit back on the counter in the 62nd minute, Chris Solly and Yann Kermorgant creating a shooting chance for Bradley Pritchard whose shot was low and wide.
Pritchard's chipped pass then handed Danny Haynes a chance from 12 yards but his first-time shot was straight at David Stockdale.
Charlton did almost steal an equaliser with five minutes left, Bradley Wright-Phillips teeing up fellow substitute Haynes for a near-post effort that was well kept out by Stockdale.