Juan Mata scored the opening goal for the Red Devils in the 65th minute. Manchester United dominated the proceedings of the match for almost the entire 90 minutes and deserved the three points.
Unfortunately for Jose Mourinho, Arsene Wenger double substitutions did wonder for the Gunners as Giroud scored the goal from Alex-Oxlade Chamberlain's cross.
Arsenal remain at the fourth position in the league table with the draw. They are yet to lose a game in the English Premier League since their opening day defeat against Liverpool.
Manchester United, on the other hand, are placed at the sixth position, six points less that fourth-placed Arsenal.
Here are some photos from the match.
Juan Mata celebrates after scoring the opening goal for Manchester United.
Juan Mata scores the opening goal for Manchester United in the 65th minute.
Olivier Giroud converts a header in the 88th minute to equalise for Arsenal.
Olivier Giroud celebrates after scoring the equaliser for Arsenal.
Ander Herrera (left) and Alexis Sanchez
Arsenal's Alexis Sanchez goes past Manchester United midfielder Ander Herrera.
All photos are take from Premier League, Arsenal and Manchester United Twitter handle)