Ryan Flynn and John Brayford struck midway through the second period in front of over 30,000 fans at Bramall Lane as United continued their recent resurgence under Nigel Clough.
Despite being denied a Sheffield derby, a large crowd turned out and the majority will have gone home delighted after booking a place in the last four and a trip to Wembley.
Charlton's Callum Harriott, who scored in the 2-1 win over Sheffield Wednesday in the last round, ought to have put the visitors in front five minutes before Flynn's opener, but somehow shot wide of an open goal from 12 yards.
Harriott and Charlton were made to rue that miss as Flynn got on the end of a Jose Baxter delivery to stab the ball home, before Brayford's deflected strike two minutes later put the result beyond doubt as United reached the semi-finals for the first time in 11 years.
With such a huge prize at stake, both sides were tentative in a cagey opening, Harriott having the first meaningful shot on goal in the 22nd minute which was easily dealt with by home goalkeeper Mark Howard.
As the Championship side pushed forward, Marcus Tudgay stretched Howard further eight minutes later, sending in a low drive from the edge of the area that had the former Arsenal trainee diving low to his left to parry away.
The hosts finally threatened as half-time approached, Conor Coady seeing his strike disallowed for offside before Bob Harris fizzed an effort narrowly over the crossbar from 20 yards in stoppage time.
United picked up where they left off in the second half, Harry Maguire producing a neat turn inside in the box before firing his effort low into the side-netting.
On the hour, Harriott missed a glorious opening to put the visitors ahead.
Johnnie Jackson's quickly-taken free-kick found Tudgay all alone on the right-hand side of the area and as Howard rushed from his goal, the forward hooked the ball back towards Harriott who, on the stretch, stabbed his effort wide of an open goal from 12 yards out.
Charlton were made to rue that miss immediately as the hosts struck twice in two minutes to send Bramall Lane into raptures.
First, Baxter's deep cross from the left was met at the back post by Flynn, who did well to leap and adjust his body to prod the ball home from six yards.
Before the visitors could recover, the advantage was doubled as Brayford's strike from 25 yards deflected off former Sheffield Wednesday man Richard Wood, completely wrongfooting Ben Hamer and trickling into the net.
Charlton were stunned and could not recover as United comfortably saw out the remaining minutes to seal a ninth successive victory in all competitions, sparking scenes of jubilation at the final whistle.
