Fabregas had a shot deflected just wide but United were threatening themselves and Almunia needed to save well from Ji-Sung Park.
Ji-Sung Park scored the only goal of the game which ensured United leapfrog the Gunners at the top of the Premier League table.
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Ji-Sung Park hit the post for United before Rooney rose to head the outstanding Antonio Valencia's cross past Friedel with 16 minutes left.
After Gabriel Agbonlahor hit an early chance straight at Edwin van der Sar, Ashley Young's tackle prevented Ji-Sung Park from giving United the lead.
As both sides traded blows, Ferguson made a change on the hour when he sent on Paul Scholes and Gabriel Obertan for Berbatov and Ji-Sung Park.
Ferguson insisted players such as Hernandez, Darron Gibson, Antonio Valencia and Ji-Sung Park should have been good enough to carve out opportunities against the Scottish champions.
Ferguson, cutting an increasingly desperate figure as he prowled his technical area, brought on Darron Gibson for Ryan Giggs and, later, Ji-Sung Park for the anonymous Macheda.
United were denied what was a clear penalty eight minutes before the interval when Ji-Sung Park tumbled under Joan Capdevila's challenge, but German referee Wolfgang Stark waved away the appeals.
United began to lose some of their early momentum, but Sorensen still had to be alert to deny Ji-Sung Park before Ronaldo tested the Danish keeper from distance.
United added to their first-leg lead through Ji-Sung Park after eight minutes before Cristiano Ronaldo scored with a 40-yard free-kick three minutes later to all but end Arsenal's challenge.
United - playing their first 3pm kick-off at Old Trafford since New Year's Day - began to find some rhythm and Ji-Sung Park scooped a close-range shot over the top.
United then held sway and snatched a deserved winner on the hour when Darren Fletcher's cross deep into the heart of the Liverpool penalty area was headed in by Ji-Sung Park.
The game was only two minutes old when Barcelona keeper Victor Valdes fumbled Ronaldo's free-kick, and only the crucial intervention of former United defender Gerard Pique prevented Ji-Sung Park turning in the rebound.
Tosic increases manager Sir Alex Ferguson's options on the left wing with Ryan Giggs and Nani already battling it out in that position although in recent weeks Ji-sung Park has also played there.
While Inter's attackers were struggling to make friends with the ball, their defenders were faring little better and were lucky to get away with a Giggs through-ball to Berbatov, who failed to cross to the unmarked Ji-Sung Park.
Arsenal continued to press forward looking for a way back into the match, but once again they were caught on the break as this time Korean Ji-Sung Park burst through a huge gap in the home defence to slide home the decisive third goal early in the second half.
Lee-Young-pyo's intervention allowed Park Ji-sung to bisect both Greece centre-backs with a perfectly weighted through ball for Park Chu-young.
The 2004 European champions rarely threatened a well-organised and extremely athletic display from South Korea, who impressed with goals in either half from Lee Jung-soo and Park Ji-sung.
If Chelsea harboured any ambition of turning the game on its head, it was short-lived as Park Ji-sung restored United's lead seconds later to clinch a meeting with either holders Inter Milan or Schalke 04 in the last four.
The early fillip allowed South Korea to dictate the tempo of the first half, with full-backs Lee Young-pyo and Cha Doo-ri pushing forward at every opportunity, while British-based duo Park Ji-sung and Ki Sung-yueng dominated the experienced Greek pairing of Karagounis and Katsouranis in midfield.
However, the 18-year-old Italian, who scored crucial goals in United's title run-in last season, was largely ineffective and was replaced in the 65th minute by Park Ji-Sung.
Evra headed home Park Ji-Sung's cross to break the deadlock before half time after hesitancy from Ali Al Habsi.
The attacking midfielder follows in the footsteps of South Korean star Park Ji-Sung, who spent seven hugely successful years at the club.
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Patrice Evra, Gary Neville, Park Ji-Sung and Paul Scholes were warming down when they were asked to move by groundstaff, sparking a row.
William Blything shouted abuse at Queens Park Rangers' Korean captain Park Ji-Sung and Everton forward Victor Anichebe at Loftus Road on 21 October.
"I would like Park Ji-Sung to become a symbol of challenge for all Koreans, " 30-year-old Kim Young Woo, who is a great fan of Park, said.
Earlier on Wednesday, they were denied a victory in Seoul as Manchester United midfielder Park Ji-Sung scored a late equalizer to give South Korea a 1-1 draw.
John O'Shea and Park Ji-Sung both had good opportunities blocked in the box, while Zenit keeper Vyacheslav Malafeev did well to deny Rooney with the minutes ticking down.
South Korea started the match brightly and took the lead on 23 minutes after Japan defender Yasuyuki Konno brought down Manchester United star Park Ji-sung in the penalty area.
Park Ji-sung was denied an excellent goalscoring opportunity when he was penalised for a foul on Giourkas Seitaridis by New Zealand referee Michael Hester, although replays suggested there was no contact between the two players.
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