The Warwickshire batsman stroked a confident unbeaten 64 to help his side post 249-7 against Nepal in Queenstown, New Zealand.
A flurry of wickets had put the Scots in trouble until Coleman dug in to help them recover from a precarious 190 for seven. Safy Sharif also played his part with a 17-ball 25 not out as Scotland added 60 runs in the last five overs before going on to complete a 90-run win.
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Kyle Coetzer, the captain, refused to get carried away with the first win of his side's qualifying campaign following their shock opening defeat by Hong Kong. He said, however: "It was a good solid performance today and we were much closer to where we want to be. We know there are still areas where we can improve."
Calum MacLeod had given his team an ideal start, hitting six boundaries in his run-a-ball 46, only for the middle order to get bogged down in tricky batting conditions.
But Coleman's battling knock, featuring four boundaries and the only maximum of the innings, gave Scotland a defendable total.
Yorkshire's Iain Wardlaw claimed three wickets for the second match in a row while Robe Taylor and Majid Haq had two apiece, the latter conceding only 24 runs from his ten overs. Guyanendra Mulla top-scored for Nepal with 34 but Scotland were comfortable winners in the end.