The Gunners took the lead when Andrei Arshavin released a powerful shot after 40 minutes, to take a stranglehold on the game.
But 14 minutes after the break, Wayne Rooney was awarded a spot kick that he converted to level the score.
On 64 minutes, Diaby's headed clearance accidently ended in his own team's net to help Alex Ferguson's men claim valuable three points.
United are now in third spot on 9 points, while Arsenal, who have one more game in hand, are fifth with six points.
The first half saw Arsenal control the game with their free-flowing football.
They were about to double their lead when they were in front shortly after the break, but United keeper Ben Foster skillfully prevented Robin van Persie from scoring.
The home side tightened their grip on the game after taking the lead, and Arsenal were struggling with defensive lapses throughout the second period.
Dimitar Berbatov was about to ensure United's lead with a last-gasp goal when he went one on one with the keeper, but his shot went well wide of the mark.
Arsenal boss Arsene Wenger was dismissed for objecting to the referee's decision, when he disallowed a late equalizer deep into injury time for offside.
The match's goals
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تقرير: بعد تعافيه.. عودة كومباني إلى مقر بايرن ميونخ
كوكوريا: لم أتحدث مع لامين يامال بعد الكلاسيكو.. أفضل الصمت والقيام بعملي
"لم يحقق الطموحات".. جينك يعلن رحيل توروب عن تدريب الفريق
إندريك: سأبذل قصارى جهدي دائما من أجل ريال مدريد.. وجاهز للأولمبياد أو أي مكان
موندو ديبورتيفو: برشلونة يستعيد داني أولمو أمام فياريال
توتي: روما كان نقطة انطلاق محمد صلاح.. وتوقعت رحيله
مساعد جوارديولا السابق يتولى تدريب ليون خلفا لـ فونسيكا
كورتوا يخوض تجربة استثمارية جديدة من خلال رياضة البادل










خبر في الجول - بعد إتمام الاتفاق.. تامر مصطفى ينضم إلى معسكر المنتخب