The Latics deserved their success as they carved out a number of openings and hit the woodwork twice against an off-colour Cherries side.
Oldham's Shefki Kuqi drilled the first chance off target before Bournemouth full-back Scott Malone forced a save from Alex Cisak.
Kuqi went desperately close on the half-hour when he headed Taylor's free-kick against the crossbar, but Cisak denied the visitors by clawing Shaun MacDonald's effort off the goalline.
Kieran Lee almost put Oldham in front before half-time and turned provider in the 52nd minute, crossing from the right to give Taylor a straightforward finish from four yards.
Tom Adeyemi missed a clear chance to double the lead and Bournemouth had another escape when Youssouff M'changama rattled the crossbar from fully 30 yards.
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