Ole Gunnar Solskjaer's side scored two fine goals at Leicester and Bruno Fernandes was superb again, but conceding quickly after going ahead both times proved costly.
Languishing 15th in the Premier League, Arsenal attempt to end a seven-game run without victory. Chelsea, meanwhile, will move within three points of leaders Liverpool with a win.
Leicester and Man United drew 2-2 at the King Power Stadium. United twice led, but the Foxes fought back on both occasions with an 85th-minute Axel Tuanzebe own goal earning a point.