New Zealander Piers Francis opened his account with a penalty for Michael Bradley's men following his move from the Chiefs at the end of November.
But penalties from Gaëtan Germain and Olly Barkley saw Edinburgh slip to their fourth consecutive defeat in the Heineken Cup, ending their hopes of progressing further.
Meanwhile, fellow RaboDirect PRO12 side Connacht fared little better as they fell to a 17-0 defeat away to Biarritz at a wet Parc des Sports Aguilera.
France international Dimitri Yachvili got things underway with a penalty, but Iain Balshaw's try before half-time meant the writing was on the wall for Eric Elwood's men.
And Seremaia Burotu's late try for the hosts secured victory, all but ending Connacht's chances of qualification to the knock out stages.
Guinness PRO12
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