The team skipped by Kyle Smith established an early lead and did not allow the Russians to score a point until the eighth end, by which time gold was effectively secured.
Smith said: "We've had a good week and a good year. I was bit nervous but that's only natural. We played everything we could and didn't give them much of a chance."
Their win meant more world joy for the Muirhead family, with Tom Muirhead taking a win to match sister Eve, who won four world junior titles between 2007 and 2011.
Scotland's women's team were due to bid to make it a double later on Sunday when they also faced Russia in their final.
Scotland women failed to join their male counterparts on the top of the podium after Hannah Fleming's team suffered a 6-5 extra end defeat to Russia in their gold medal match.