Through religion comes power, but at a cost. One becomes tethered by the same trials that your deity possesses, their weakness is your weakness, their enemies are your enemies. Why do you think I aligned to Dol Dorn? You know his weakness is? Nothing. He fights weakness morning, midday, and night.
The process is simple: Find out which of the gods the demon worships and snag a holy symbol from the opposing faction. During your battle with the creature, force them into a corner and simply brandish the holy symbol towards them, weakening them and containing them.
From there on, it's your choice what to do. Bring a carbonated beverage to sip on, or perhaps catch up on some new trade journals while you wait for the demon's powers to sufficiently wane. I can also recommend doing all of this over some tarping so you can collect the demon's blood (great for staining dark hardwoods such as black walnut. It also transfers amazing fire-resistant properties to the wood).