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United had the better of the opening stages and had their first real attempt on goal after 16 minutes when Danny Welbeck fired straight at Petr Cech on the angle.
The visitors continued to look more comfortable on the ball and they were rewarded with 22 minutes on the clock when Oriol Romeu was dispossessed before Giggs slotted in.
Chelsea rarely threatened but they found themselves level on 35 minutes when Luiz converted from the penalty spot following Alexander Buttner's foul on Victor Moses.
However, the Red Devils had the final say of the half thanks to Hernandez's composed finish from Anderson's through ball on 43 minutes.