Trailing 2-1 from the first meeting of the sides in Italy last week, Sir Alex Ferguson's side needed to score at least once on home soil to set up a last four meeting with either AC Milan or Bayern Munich.
But a dominant United went for the jugular from the start and produced a sensational three-goal blast inside the opening 20 minutes before adding insult to injury with a fourth on the stroke of half-time.
That effectively killed off the game and the Red Devils kept their foot on the gas after the interval to notch two more classy goals, before AS Roma pulled back a consolation effort which drew ironic cheers from the jubilant Old Trafford faithful.
But once again United struck back to score a late seventh which overwhelmed the side currently placed second in the Serie A table and left the much-fancied Italians totally shell-shocked and on the wrong end of an 8-3 aggregate scoreline.
The home side had opened the scoring in the 11th minute through the unlikely source of Michael Carrick.
Man-of-the match Cristiano Ronaldo toyed with his marker before squaring a pass inside to the England midfielder, who dinked a superb right-foot shot from 25 yards over Alexander Doni with the goalkeeper well off his line.
That drew United level on aggregate in the tie and heading into the semi-finals on the away goal rule, but in a performance of high energy and superb commitment they were never going to settle for that.
Ryan Giggs rolled back the years with a vintage performance roaming across the pitch and Alan Smith was on the end of his first-time pass to double the advantage with a precise finish after 17 minutes.
Wayne Rooney was next to profit from the veteran Wales international as he ghosted in front of his marker to guide the ball home from inside the six-yard box, after a pinpoint Giggs cross from the right two minutes later.
On the stroke of half-time, Ronaldo got himself on the scoresheet to cap a superb first-half display from the Portugal international.
Ronaldo was afforded acres of space down the right and, after running at the retreating Cristian Chivu, lashed a low shot from the edge of the box between the keeper and his near post.
After the interval and with a half-time party atmosphere enveloping Old Trafford, United made it 5-0 when Giggs again delivered a brilliant cross from the left and, after Smith failed to make contact, Ronaldo was on hand to stab it home from close range.
On 60 minutes it was 6-0 as Roma failed to close down Carrick and he shaped a superb 20-yard shot into the top corner after a Gabriel Heinze cut-back.
Daniele de Rossi reduced the arrears with a classy volley after 69 minutes, but substitute Patrice Evra had the final say with a low shot in off the inside of the post nine minutes from full-time, to confirm United's largest ever Champions League victory.