Bangladesh crushed Zimbabwe by eight wickets in the first of five one-day internationals at the Queen's Sports Club on Sunday.
The left-arm spin bowling of Ray Price was in particular meat and drink to Ashraful, who continually smacked him to the boundary.
The seamers were also unable to cope as Ashraful took his one-day career total beyond 3,000 runs.
Ashraful and Tamim Iqbal shared a partnership of 137 with Bangladesh wrapping up victory with more than 15 overs to spare.
Bangladesh arrived in Zimbabwe having won the Test and ODI series in the West Indies.
The second match is on Tuesday and the third on Friday.
"It was a long journey from the West Indies. We were flying for nearly two days," said skipper Shakib Al Hassan on the eve of the game on Sunday.
Bangladesh only had one warm-up game before the opening ODI which the tourists lost to Zimbabwe 'A'.
"Obviously there was a bit fatigue when we took the field against Zimbabwe A. Our kits also arrived at the last moment," said the captain.
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