The play of the match came when Bangladesh's Rubel Hossain made an outstanding catch at the long-boundary to dismiss Nawroz Mangal for 27.
Earlier, fast bowler Mirwais Ashraf took Afghanistan's first World Cup wicket, having Tamim Iqbal (19) acrobatically caught by wicketkeeper Afsar Zazai to end a 47-run opening stand. Bangladesh slipped to 52-2 when Ashraf struck again, trapping Anamul Haque (29) lbw, and to 119-4 in the 30th after Shapoor Zadran (2-20) removed Soumya Sarkar (28) and Mahmudullah (23).
Veterans Mushfiqur (71) and Shakib (63) restored the innings for Bangladesh before both were dismissed in a late collapse, with Afghanistan taking three wickets in the last seven balls.
Bangladesh, which has been playing at the World Cup since 1999, was under intense pressure entering the match as the established team in cricket's elite against a team that started almost from scratch in the last two decades.
Afghanistan, 12th in the ICC rankings and which won its only previous one-day international against Bangladesh at the Asian Cup last year, showed nerves and inexperience when it failed to refer at least two questionable umpiring decisions to the third umpire and gave away too many runs for overthrows from basic fielding errors.
And in the 33rd over, leg spinner Samiullah Shenwari, who scored 42 runs for Afghanistan before being run out, had to be taken out of the attack after bowling just seven balls when he failed to heed a caution from the umpire for running on the pitch after his delivery.
Afghanistan will next play Sri Lanka on Sunday in Dunedin, New Zealand. Moles says his side won't be excited just to be there.
"I think we've moved past that," Moles said. "We're here to compete in the group games. We haven't disgraced ourselves, but that wasn't a true reflection of the work that we do in preparation and the way we play our cricket.
"Tonight ... we just didn't get out of the blocks with the bat. We were in a fog, we just didn't get going and they bowled very well. Before we knew it we were one, two, three down ..."
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