The home side were on top before defender Robbie Neilson, previously booked for a foul on Samaras, was shown a straight red in the 28th minute for leading with an elbow in an aerial tussle with the Greece striker.
The game turned on that incident and in a one-sided second half the home side were put to the sword.
Ledley, Samaras and Stokes racked up an unbeatable lead before Hoops skipper Brown scored from the spot a minute from time after Samaras had been tripped by Sean Dillon in the United box.
Celtic remain on course for the treble but United will wonder what might have happened had the experienced Neilson not left referee Iain Brines without an option.
Celtic boss Neil Lennon, who continued his self-imposed media ban after taking exception to comments made about his club in regard to the situation at Rangers, saw his side play second fiddle to United until the game took that dramatic twist on 28 minutes.
In yesterday’s other quarter-final tie, last year’s beaten finalists Motherwell lost 2-1 at home to Aberdeen,
Rory Fallon headed the opener after four minutes and struck a brilliant second after 41 minutes, after Michael Higdon had missed the chance to equalise from the penalty spot at Fir Park.
Nicky Law pulled a goal back 11 minutes from time, but the Dons went on to record their first win over the Steelmen in three-and-a-half years to reach the final four at Hampden.
New Zealand international Fallon said: “If that goal can lead us on to silverware that will be up there with my greats. We’ve put ourselves in a great position to try to get something.”
On Saturday, Hibs’ Roy O’Donovan and Leigh Griffiths scored first-half goals to see off First Division side Ayr United at Somerset Park and put Hibernian into the last four.
They will be joined there by either St Mirren or city rivals Hearts after an own goal from Marius Zaliukas earn Saints a 2-2 draw in Edinburgh.
Scottish Cup semi-final draw (April 14/15): Aberdeen v Hibernian, Celtic v Hearts or St Mirren.