Stanikzai hit an unbeaten 90 off 103 balls while Shinwari smashed 69-balls for 81 during their record sixth wicket stand of 164 runs after Bangladesh won the toss and put Afghanistan in to bat on a slow and dry pitch.
The Stanikzai-Shinwari stand is the third highest partnership for Afghanistan in all one-day internationals and the highest for the sixth wicket.
Stanikzai hit six boundaries and three towering sixes in his highest one-day score while Shinwari smashed 10 fours and a six. They ran riot in the final 10 overs as Afghanistan added 107 for the loss of Shinwari who was run out off the penultimate delivery.
Afghanistan had lost opener Mohammad Shahzad (two) in the third over of the innings before Karim Sadiq (12) and Najibullah Zadran (21) took the total to 40.
Left-arm spinner Arafat Sunny (2-44), who replaced injured paceman Mashrafe Mortaza, dismissed both in his successive overs.
Nawroz Mangal (24) and skipper Mohammad Nabi (seven) too failed to benefit from good starts as Afghanistan were left struggling at 90-5 in the 27th over.
It was left to Stanikzai and Shinwari to lift the innings.
Sri Lanka have won both their matches while title-holders Pakistan and India have won one of their two matches.