Jack Murphy's kicking helped bring Ulster back to within five points late on, but Edinburgh held out to take the win.
Ulster have opened their URC campaign with a 34-29 defeat to Edinburgh in Belfast.
The home side found themselves 34-5 down early in the second half before mounting a strong comeback through tries from Zac Ward, David McCann and Keynan Knox.
Jack Murphy's kicking helped bring Ulster back to within five points late on, but Edinburgh held out to take the win.
Ulster do at least leave with two bonus points from the defeat.

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