United blitzed hapless Reading in the opening exchanges as goals from Gabriel Heinze, Louis Saha and Ole Gunnar Solskjaer seemed to have ended the tie before it had started.
But Reading battled back with enormous spirit, pulling one back before half-time with a close-range header from Dave Kitson and then setting up a nail-biting finish with a brilliant diving header from substitute Leroy Lita.
And the home side came within a whisker of forcing extra time when a stoppage-time volley from Brynjar Gunnarsson smashed against the crossbar with the outstanding Edwin Van der Sar beaten.
Van der Sar had previously denied all Reading's hopes of a comeback with superb saves to keep out Seol Ki-Hyeon and then Kitson, but in the early exchanges it had appeared the veteran Dutch keeper could have taken the night off.
Argentina international Heinze started the rout, slamming a low drive under the dive of young keeper Adam Federici after great build-up down the right by Solskjaer.
Federici had been the hero of the first game at Old Trafford, so much so he was voted by player of the round by fans on the Football Association website.
But he was left red-faced by Heinze's opener and then had salt rubbed in his wounds as United hit two more in quick succession.
Saha made it 2-0 when he chested down Rio Ferdinand's long ball forward and, as Andre Bikey and Ulises De la Cruz backed off, blazed a shot beyond the helpless Federici.
Another two minutes on the clock, another goal, Solskjaer this time providing the finish with the outside of his right boot after Kieran Richardson's long ball had beaten the offside trap and allowed Solskjaer to run free.
Reading were shell-shocked, but to their credit they responded with spirit.
Kitson pulled one back for the home side midway through the first half by heading home unmarked at the far post after Ivar Ingimarsson had flicked on John Oster's corner.
And South Korea winger Seol came within a whisker of bringing Reading within touching distance on the stroke of half-time when his long-range drive was tipped around the post by Van der Sar at full-stretch.
Steve Coppell's side continued to carry the fight in the second half with Kitson seeing a shot on the turn brilliantly pushed away by the alert Van der Sar.
But Lita gave the home fans real hope when he dived headlong to steer home De la Cruz's right-wing cross.
United looked nervous at the back and so nearly paid a heavy price in the final minute when the impressive Oster teed up Gunnarsson for a powerful drive that thudded against the bar.