The debutants restricted Bangladesh to 267 all out but were then dismissed for 162 in 42.5 overs at Manuka Oval, with skipper Mohammad Nabi top scoring with 44.
Nabi???s opposite number, Mashrafe Mortaza (3-20), took three wickets for Bangladesh, who had Mushfiqur Rahim (71 of 56 balls) and Shakib Al Hasan (63 off 51) to thank for propelling them to a respectable total.
Mortaza won the toss and elected to bat but his charges trundled along in the first 29.1 overs, reaching 119-4, with Afghanistan seamer Mirwais Ahshraf and Shapoor Zadran plucking two scalps each.
However, Shakib and Mushfiqur then shared a fifth-wicket partnership of 114 ??? the pair???s fourth-century stand in one-day international cricket ??? as The Tigers moved their total on to 233 in the 45th over.
But Shakib???s departure ??? the world???s No 1 ranked all-rounder bowled by Hamid Hassan ??? led to Bangladesh losing their final six wickets for 34 runs, with Aftab Alam castling last man Taskin Ahmed with the final ball of the 50th over.
Shapoor Zadran (2-20 from seven overs) recorded the best bowling figures for Afghanistan but Samiullah Shenwari ??? who caught Mushfiqur expertly in the deep ??? got through just seven deliveries before being removed from the attack for running on the pitch.
Afghanistan ??? victorious over Bangladesh in the side???s only previous ODI ??? made a dreadful start to their reply, sinking to 3-3 within the opening three overs after losing Javed Ahmadi (1), Afsar Zazai (1) and Asghar Stanikzai (1).
Nowroz Mangal (27) and Shenwari (42) dug in for the World Cup newcomers, combining for a 62-run stand, but Mangal was then pouched brilliantly by Rubel Hossain on the leg side after attempting a slog sweep.
Rubel did himself some damage while taking the catch, limping off the field with a suspected calf injury, but the seamer saw his team-mates pick up another wicket when Shenwari was run out trying to collect a second run.
Nabi got himself in, stroking five boundaries, but then clubbed Mortaza straight to mid-off as the associate nation shipped their last five wickets for 26 runs, Alam???s run out ending the contest.
Bangladesh are next in action against World Cup favourites and co-hosts Australia in Brisbane on Saturday ??? a game in which fit-again Baggy Greens skipper Michael Clarke is expected to feature ??? while Afghanistan tackle Sri Lanka in Dunedin on Sunday.