Joe Cokanasiga scored two of Bath's five tries and Finn Russell's boot accounted for 17 points from four conversions, two penalties and a left-footed drop goal.
Sale, trying to halt a run of six successive defeats in all competitions since Christmas, were level at 24-24 on the hour but faded in the last quarter.
Bath look threatening from the off and took the lead through Matt Gallagher after just four minutes as Cameron Redpath latched on to an offload from Cokanasiga to send his full-back away, with Russell converting from wide out.
Sale sought a quick response and centre Rob Du Preez beat Gallagher to a lofted kick by George Ford but Bevan Rodd spilled a pass with the home defence stretched.
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