Champions League
April 30, 2009United, European champions last year, dominated the match for long periods but in the end only had an early header from John O'Shea to show for their superiority.
The two sides will play the second leg at the Emirates Stadium next Tuesday.
With only one goal between them, Arsenal will fancy their chances of progressing despite being outplayed for much of the match at Old Trafford.
Cristiano Ronaldo smashed a shot onto the crossbar midway through the second half, while Manuel Almunia was called on to make several important saves throughout.
Improbable hero
United had been threatening the Arsenal goal before making the breakthrough - the only surprise was that it came through the unlikely figure of O'Shea.
Michael Carrick worked his way to the by-line after a corner, but his deflected cross was headed into the net by O'Shea.
Ronaldo headed a good chance straight at Almunia, while Cesc Fabregas shot straight at Edwin van der Sar.
Wayne Rooney fired a shot just wide and Ronaldo then smashed a stunning effort onto the crossbar but United were unable to extend their lead.
On Tuesday, Chelsea played to a goalless draw against Barcelona at the Camp Nou in the other semi-final game.
Sir Alex positive
United manager Sir Alex Ferguson said that while his men didn't play to their potential, the team was nonetheless in a favorable position for the return leg in London.
"The most pleasing aspect is that before the game we said try and win and not lose a goal and we have done that and the performance level was very good so we have achieved that and I think we have given ourselves a good chance overall," Ferguson told a news conference.
"We have players who can score goals and we will be a goal threat at their ground but the tie is not over.
United defender Rio Ferdinand picked up a suspected rib fracture after colliding with Gunners forward Nicklas Bendtner in the closing stages.