The Egyptian, 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.
Alex Bruce's weak header allowed Stephens room to attack Hull through the middle but he was stopped dead by Meyler.
Jackson's left foot was looking Charlton's best weapon, with a back-post cross and a teasing free-kick both causing awkward moments in the Hull box.
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 from close range at the back post.
Only a fine defensive header from Leon Cort prevented Hull making it two on the stroke of half-time, Brady and Stephen Quinn making space on the left before the ball made its way to Meyler at the edge of the box.
The Irishman hit a fierce shot towards the centre of goal but Cort, against his former club, bravely got his head in the way.
Just a minute had passed in the second half when Hull went close again. A Brady corner was again the cause but McShane produced an air-kick with the goal gaping.
Hull were on the hunt for a second, Elmohamady giving Cedric Evina grief on the right and then drawing an unconvincing flap from Hamer.
The home side's Egyptian contingent grew to three when Ahmed Fathi replaced the injured McShane.
But Hull's rhythm was unaffected, Meyler stinging Hamer's gloves with a half-volley and Gedo heading Elmohamady's precision cross over.
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.
Gedo missed out on a second when he ran the ball out attempting to round Hamer following Robert Koren's weighted pass.
Charlton almost stole 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.
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