A moment of brilliance from Antony midway through the first half helped Erik ten Hag's side on their way to seal their spot in the final four.
Marcus Rashford confirmed the win with two late goals off the bench in stoppage time at the end of the game.
This results marks an eighth consecutive victory for the Red Devils in all competitions with the Manchester Derby next up at the weekend.
This is the first time since December 2018-January 2019 that Man United have won eight games in a row, but their biggest tests are yet to come.
For Charlton, this defeat has ended their mini unbeaten run as well as their cup exploits for the season.
Dean Holden's men will now turn their attentions back to an unlikely push for the playoffs in the second half of the League One season.
One of the big stories pre-match was the inclusion of 17-year-old Kobbie Mainoo in midfield, as the youngster came in to replace the suspended Bruno Fernandes in a more advanced role.
Soon however, it was Antony who would steal the show, as his blockbuster strike set United on their way to victory.
Receiving the ball roughly 25 yards from goal, the Brazilian wide man set himself perfectly and unleashed a stunning curling effort which left Charlton keeper Ashley Maynard-Brewer with no chance at full stretch.
Another of United's Brazilians, Fred, was another standout performer in the opening period, and he hit the post from a free-kick with the first half drawing to a close.
Alejandro Garnacho was electric for the hosts and comfortably the most dangerous threat throughout the match out wide, while it was a more difficult night for Anthony Elanga who was deployed in an unfamiliar central position up front by himself.
There were also fitness concerns for ten Hag too, as Diogo Dalot limped off on his return to the starting lineup for the first time since the World Cup break.
Despite the good form of Aaron Wan-Bissaka in his absence, Dalot had been a key performer for United in the early stages of the season, and this is a real setback on what should have been his return to regular first-team action.
There were early chances for both sides in the second half as Charlton played more adventurously, but Elanga's frustrations continued as he had a goal ruled out for offside at the other end.
Despite the slender one-goal advantage, ten Hag was confident enough to take off both Fred and Antony on the hour mark, but his decision was justified as the duo were given a well-earned rest as United saw the job through.
Rashford, who took the place of Antony, made absolutely sure of the result when he scored an injury-time brace late on, as the home side secured a fully-deserved win.
Things will get tougher for the Premier League side at the weekend when they welcome Manchester City to Old Trafford for the Manchester Derby in their next encounter.
For Charlton, they face Barnsley at The Valley on Saturday in a game that could be vital to their slim hopes of getting back in the race for the top six.