Hernandez and Park end Chelsea hopes
Mexican striker Javier Hernandez opened the scoring just before half-time and Park Ji-sung added a second just moments after Didier Drogba had given Chelsea hope with an equaliser on the night but United ran out 3-1 winners on aggregate.
Ferguson's side, who beat Chelsea on penalties in the 2008 final and had carved out a 1-0 lead from last week's first leg, absorbed plenty of pressure during an open and balanced game in which the Londoners had Ramires sent off with 20 minutes left.
The victory put United into their fourth semi in five years and left big question marks hanging over Chelsea manager Carlo Ancelotti's future now that his flagging team's only realistic chance of silverware has evaporated.
United, chasing a treble of Champions League, Premier League and FA Cup, will face Schalke 04 or Inter Milan in the last four with the German side holding a 5-2 advantage over the Italians before Wednesday's quarter-final second leg.
Ferguson singled out "incredible" old-timer Ryan Giggs for an outstanding game in the centre of midfield from where he set up Hernandez's 43rd-minute opener while adding that the Mexican had almost not started as he had toyed with a different lineup.
"We had two teams picked tonight and hopefully I picked the right one, I'm not sure I did pick the right one," Ferguson told a news conference.
"The other option is to play Park in that position and Wayne (Rooney) up top, leaving Chicha (Hernandez) out. That's where you get luck, Chicharito scores the first goal."
While the loud taunts from United fans to Chelsea manager Carlo Ancelotti of "You're getting sacked in the morning" were possibly wide of the mark, the Italian is under pressure now his side's last realistic chance of silverware has vanished.
"I'm not concerned," he told a news conference when asked if he was worried about his job given owner Roman Abramovich, who was watching from the stands, has been quick to show the exit to previous managers who finish a season without a trophy.
"I have to work, I have to try to do my best. It is not my decision to stay or not stay," said Ancelotti.
Although Chelsea started brightly their cause was not helped by striker Fernando Torres' apparent lack of confidence in front of goal, which seems to be growing with every match that goes by without him breaking his scoring duck at the club.
Ancelotti said he had "maybe" made a mistake in starting Spain forward Torres, whom he replaced with Drogba for the second half with the Ivorian immediately sharpening things up.
Torres left the field to loud jibes of "What a waste of money" as United fans revelled in his failure to score since his 50 million pounds British record transfer in January from arch rivals Liverpool.
Chelsea, the last team to win at Old Trafford a year ago en route to the Premier League title, looked hungry for a repeat with Nicolas Anelka shooting just wide after a quarter of an hour and Torres also squandering a couple of chances.
It was, however, United who got the ball in the net first in the 26th minute with Hernandez's diving header from a Rooney cross only for the linesman to flag for offside even if it took some time for the jubilant home fans to realise it.
That frustration was forgotten two minutes before the break when John O'Shea sent a reverse pass to Giggs on the wing and the evergreen Welshman slid a pinpoint ball across the area where the lurking Hernandez, ruled just onside, crashed it into the roof of the net from virtually under the crossbar.
It was Hernandez's 18th goal of the season for United and came at the worst possible time for Chelsea.
When Ramires was sent off for fouling Nani after 70 minutes Chelsea's hopes looked shot but a fired-up Drogba had other ideas when he controlled a ball with his chest and unleashed a right-footed shot under Edwin Van der Sar in the 77th.
Any hope Chelsea had of United buckling were snuffed out immediately, however, as Park netted 21 seconds later to calm the home side's nerves and give the Londoners another entry to their catalogue of wretched Champions League moments.