Leon Best had given the hosts hope of booking a FA Cup quarter-final clash with rivals Sheffield United, only for the striker's close-range header to send the Addicks through
There had been much talk of the possibility of a Steel City derby in the build-up to Monday's fifth-round clash - rescheduled due to a waterlogged pitch - but Church's second-half header dashed Wednesday's hopes as Charlton reached the last eight of the competition for the first time in eight years.
Callum Harriott had put the visitors ahead midway through the first half with a sweetly struck effort from just inside the area as Wednesday looked edgy in front of their home fans.
Wednesday improved in the second half in the all-Championship tie, Leon Best firing home as Charlton failed to deal with a free-kick in the 57th minute, but parity lasted just eight minutes as Church got on the end of Johnnie Jackson's set-piece to head home and put his side within 90 minutes of a Wembley appearance.
Both sides made numerous changes from the weekend and it was the visitors who coped better with the disruption in the opening stages, Astrit Ajdarevic scuffing an effort narrowly wide of the post after excellent work down the left from Harriott.
It was Harriott who gave Charlton a deserved lead in the 22nd minute, lashing a loose ball into the top left-hand corner from 15 yards after Wednesday had failed to deal with a low ball into the box.
Wednesday grew into the game gradually as the half wore on, Gary Gardner forcing a first save out of Ben Hamer with a rasping 25-yard volley six minutes before the interval. Best also tested Hamer with a dipping strike three minutes later.
The home side began the second period with greater conviction, Giles Coke firing off target after robbing Diego Poyet on the edge of the box.
Charlton responded well as captain Jackson, who scored a last-minute winner against QPR on Saturday, fizzed a low effort narrowly wide of the right-hand post from distance.
Best pulled his side level shortly before the hour-mark as he slammed the ball home via the aid of a slight deflection after Manuel Llera knocked down Chris Maguire's free-kick.
Wednesday ought to have gone in front a minute later, substitute Atdhe Nuhiu getting his header all wrong following another dangerous Maguire set-piece.
The hosts were left to rue that miss in the 65th minute when Jackson swung in a free-kick from the right and Church was left all alone to head beyond Damian Martinez from six yards out.
Nuhiu went close again with 17 minutes remaining, seeing his header rebound off the inside of the post before Hamer managed to claw the ball away from on the goalline.
Wednesday had a flurry of late chances, Hamer diving at the feet of Best before Nuhiu headed over and Maguire saw his deflected shot brilliantly tipped behind.