Goals from Fabio da Silva after 28 minutes and a 49th minute header from Wayne Rooney put United through to a record 27th semi-final which will be at Wembley Stadium next month.
The victory was a huge boost for Sir Alex Ferguson's Premier League leaders before their Champions League last-16 second leg against Olympique Marseille back at Old Trafford on Tuesday after two successive League defeats by Chelsea and Liverpool.
United will be aiming to reach the quarter-finals of Europe's premier competition after their goalless draw in the first leg three weeks ago to keep alive the chance of repeating their European Cup, FA Cup and Premier League treble of 1999.
For Arsenal the night ended in yet more disappointment following their elimination from the Champions League by Barcelona on Tuesday and their defeat by Birmingham City in the League Cup Final at Wembley on February 27.
Arsenal manager Arsene Wenger told reporters: "I believe that sub-consciously the disappointment of Tuesday night has played a part today in the game, something has gone, not in our effort or our attitude but in our confidence."
He added: "They (United) were much more clinical and we have had a very difficult week but the team will recover from that and refocus."
He also said Swiss defender Johan Djourou, who suffered a dislocated shoulder near the end of the match, would be out for the rest of the season.
Arsenal are second behind United in the Premier League title race, and could still salvage something from a season that promised so much just two weeks ago, but they will need an enormous improvement in their form and confidence to do that.
Before their shock defeat by Birmingham they were chasing four trophies but their hopes of ending a six-year trophy drought are hanging by a thread.
THRILLING MATCH
In Saturday's other quarter-final, Bolton Wanderers won 3-2 at Birmingham to clinch a place in the semi-finals for only the second time since they last won the FA Cup in 1958.
They sealed their victory after a thrilling match with a 90th minute header from South Korean forward Lee Chung-yong after Birmingham had twice fought back to equalise.
Johan Elmander and Kevin Davies, with a penalty, scored to put Bolton 1-0 and 2-1 ahead, while Cameron Jerome and Kevin Phillips, with a brilliant strike, got Birmingham's equalisers.
Unusually for United and Arsenal, both teams went into the game with plenty to prove after recent poor results, but United manager Ferguson and his old rival Wenger were forced to shuffle their sides due to injuries to key players.
Ferguson fielded seven defenders in his starting line-up while Wenger was without injured captain Cesc Fabregas, goalkeeper Wojciech Szczesny and the influential Alex Song.
But it was United who made the breakthrough with a flowing move midway through the first half.
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