O’Shea scored from close range after Arsenal failed to clear a corner – giving United a slender but fully deserved advantage to take into the semi-final second leg at the Emirates next Tuesday.
Sir Alex Ferguson has made it his mission to make United the first side to successfully defend the Champions League title and they set about their old Premier League adversaries with relish from the first whistle.
And, while United will be happy to go to Arsenal in the ascendancy and having prevented Arsene Wenger’s side from scoring a crucial away goal, they will have regrets that they failed to capitalise on the superiority they exerted throughout.
Arsenal were penned in for long periods as United played at the high tempo that suits them best, and it was only a mixture of the excellence of goalkeeper Manuel Almunia and good fortune that kept the deficit within manageable proportions.
Almunia saved superbly from Wayne Rooney, denied Carlos Tevez with a double block and turned away Cristiano Ronaldo’s header from six yards as United turned on the style in a dazzling first 45 minutes.
Arsenal managed to steady the ship after the interval, but they never seriously threatened United apart from a tame Cesc Fabregas shot and a volley from Emmanuel Adebayor after the break.
Ronaldo struck the bar from 30 yards with 20 minutes remaining as United continued to press for what could have proved a decisive second goal, but Arsenal survived and will still feel there is life in the tie yet, despite delivering a disappointing performance.
United never allowed Arsenal to get into their trademark passing rhythm, playing with more drive and energy than the Gunners, who were overrun in midfield at times and struggled to cope with the pace and variety of Rooney, Tevez and Ronaldo in attack.
Ferguson prefaced the game by suggesting it could be the “perfect semi-final” – it was not quite that for United, but you suspect they will be highly satisfied with the outcome.
United’s fans certainly celebrated at the final whistle in a manner that suggested they feel they have taken a significant stride towards retaining the trophy they won so dramatically on penalties against Chelsea in Moscow last May.
Wenger, however, will harbour hopes that the undoubted talent in his side, kept under wraps for so long here, can turn things around on home territory.
Ferguson’s selection of Tevez ahead of Dimitar Berbatov suggested he wanted an energetic, high-tempo approach against an Arsenal defence undermined by injuries to influential pair William Gallas and Gael Clichy.
And that was exactly what he got in thrilling opening exchanges completely controlled by United and played out in a vibrant Old Trafford atmosphere.
Arsenal goalkeeper Almunia was in action inside the first 90 seconds, retreating desperately towards his goal to claw out Rooney’s looping header.
And youngster Kieran Gibbs then showed early nerves as he slipped to let in Ronaldo, but United’s winger flashed the ball across the face of goal with no-one on hand to apply the crucial final touch.
Arsenal were on the ropes, and it took a superb double save from Alumnia to deny Tevez after a slick exchange with O’Shea as United swarmed all over a Gunners side struggling to come to terms with the pace of the game.
Wenger’s players never looked like surviving this fierce early barrage, and so it proved as United took a deserved lead in the 18th minute.
Arsenal failed to clear a corner, and when Michael Carrick’s cross was deflected into his path by Mikael Silvestre, O’Shea lashed a finish high past Almunia.
Arsenal’s only response was a low 20-yard shot from Fabregas that was comfortably collected by Edwin van der Sar.
Almunia was the keeper in constant action, and he performed heroics again after 28 minutes to keep out Ronaldo’s header from an inviting cross by the industrious Tevez.
The only black spot in the opening 45 minutes for United – apart from not capitalising fully on their outstanding approach play – was a yellow card for Tevez after he collided with Almunia in a chase for possession.
Arsenal looked to have settled more after the break, and even felt bold enough to pose another brief threat after 62 minutes when Adebayor’s volley flew over the top, although Van der Sar had the effort well covered.
United made a double substitution with 25 minutes left, sending on Ryan Giggs – making his 800th appearance for the club – and Berbatov for Anderson and Tevez.
And Ronaldo almost marked their arrival with United’s second as he sent a thunderous right-foot shot against the crossbar with Almunia motionless.
Wenger made a change of his own, replacing the subdued Theo Walcott with Nicklas Bendtner, and then sent on Eduardo for Adebayor as the game entered its final 10 minutes.
The changes made little alteration to the pattern of the game, with Arsenal ultimately content not to concede a second after some harrowing moments.
It is advantage United – who suffered a scare late on when Rio Ferdinand went off after suffering a blow to the ribs – but the narrow lead still leaves the semi-final in the balance ahead of next week’s return game.
BBC Sport Player Rater man of the match: Arsenal’s Manuel Almunia (7.57 on 90 minutes).
Please note that you can still give the players marks out of 10 on BBC Sport’s Player Rater after the match has finished.
Man Utd: Van der Sar, O’Shea, Ferdinand (Evans 87), Vidic, Evra, Fletcher, Carrick, Anderson (Giggs 66), Ronaldo, Tevez (Berbatov 66), Rooney.
Subs Not Used: Foster, Park, Scholes, Rafael Da Silva.
Goals: O’Shea 18.
Arsenal: Almunia, Sagna, Toure, Silvestre, Gibbs, Song, Diaby, Walcott (Bendtner 70), Fabregas, Nasri, Adebayor (Eduardo 82).
Subs Not Used: Fabianski, Denilson, Ramsey, Djourou, Eboue.
Ref: Claus Bo Larsen (Denmark).