Stanikzai and Shenwari shared 164 runs for the sixth wicket to propel Afghanistan to a challenging total after they were reduced to a precarious 90 for five in the 27th over after being put into bat at Khan Shaheb Osman Ali Stadium.
The duo, who started cautiously, finished with a flourish as they punished Bangladesh bowlers in the final 10 overs by collecting 107 runs.
But after reaching the milestone the 26-year-old cut loose as he carted the hosts' bowlers all around the park. Stanikzai's 90-run knock came off 103 balls and included six fours and three sixes.
Shenwari, on the other hand, maintained a brisk scoring rate throughout. He made 81 off just 69 balls, including 10 fours and a six.
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The Bangladeshi bowlers did not get support from their fielders who dropped two catches in the innings.
Earlier, Afghanistan openers Mohammad Shahzad (2) and Karim Sadiq (12) departed cheaply. Shahzad was foxed by a slower one from pacer Rubel Hossain and was trapped in front of the wicket, while left-arm spinner Arafat Sunny claimed the scalp of Sadiq who handed a simple return catch to him.
Next batsman Nawroz Mangal, however, showed some purpose as he hit three fours in his 33-ball 22 before being out in the 23rd over. Afghanistan lost another wicket soon after with skipper Mohammad Nabi dismissed for just seven as the visitors were further reduced to 90 for five inside 27 overs before Stanikzai and Shenwari took them to a respectable total.