Bradley, who spent eight years in charge at Connacht, now finds his side below his former employers in the table and in a dire run of form after losing their last five RaboDirect PRO12 games.
Connacht, meanwhile, followed up on last weekend's 13-13 draw with Glasgow Warriors - a result that ended their own run of ten league defeats - with a win that Elwood has been waiting for.
And with Scarlets next up for the Galway outfit former Ireland international fly-half Elwood can't wait to see his troops back in action.
He said: "We will take a lot of confidence from the win. This win will give momentum. We head to Scarlets next week but we will go there with some confidence now after this win.
"The lads did not panic when Edinburgh got a couple of tries and I felt we showed a lot of composure from there to the end."
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