Bucs got off to a perfect start when Nigerian midfielder Onyekachi Okonkwo drew first blood in the second minute with a curling shot.
Mbesuma then missed an opportunity eight minutes later as his effort was parried away for a corner.
However, Mazembe showed they were not down and out as they drew level on the stroke of halftime through Kabangu Muloto in the 44th minute.
This was after a cross by Tresor Mputu for Samatta who headed across goal for Kabangu to supply the easy finish.
The two teams went for a break with the score at 1-1.
After the interval, Mbesuma got on the scoresheet in the 56th minute with a tap in after a cross from Khethowakhe Masuku to give Pirates a 2-1 lead.
Namibian international Rudolf Bester had a chance to get a third for Bucs, but fluffed the opportunity in a one-on-one situation in the 67th minute.
Pirates had the last say, though, as Mbesuma slotted a penalty to make it 3-1 at the death.
The Zambian international had been brought down by the keeper.
Orlando Pirates XI: Meyiwa, Jele, Phungwayo, Lekgwathi, Gcaba, Maselesa, Okonkwo, Segolela (Klate 83rd), Bester (Makola 77th), Masuku (Mabena 90th), Mbesuma
TP Mazembe XI: Kidiaba, Nkulukuta (Ndonga 27th), Kasusula, Himonde, Boateng, Kabangu, Adjei Nii (Sinkala 66th), Ilongo, Kalaba, Mputu (Asante 77th), Samatta