After restricting the Africans to a manageable total of 109 for eight, the Asian batsmen kept their cool in reaching the target for the loss of four wickets in 15.5 overs.
Bangladesh's pocket dynamo Tamim Iqbal led the victory charge early on with a quick-fire 30 off 22 balls, including three fours and a six, before he stepped out to spinner Thandi Tshabalala and was easily stumped.
Iqbal had steadied the rocking Asia boat with a stand of 27 with Tillekaratne Dilshan, who cracked an unbeaten 47 in only 36 balls with a six and six fours embellishing it, after Asia XI were in a spot of bother at 34 for 3 in the sixth over.
There was enough firepower in the experienced Asia line-up to weather the cheap dismissals of Pakistan's Imran Nazir and Kamran Akmal and Bangladesh's Mohd Ashraful to cruise home comfortably.
Dilshan and Asia captain Shoaib Malik (14 not out in 18 balls) ensured the momentum was maintained with a stand of 49 runs in 36 balls for the fifth wicket after coming together with at 61 for four.
The battle-hardened duo gathered runs at a fast clip with both clouting sixes off the hapless Africa bowlers who showed they were not experienced enough to take on batsmen of their class.
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