Two late goals eased the pain for the Faroese players, but they were outclassed in Torshavn and were five goals down after 29 minutes. Scotland next play Bosnia-Herzegovina at Fir Park on Thursday night.
While at fault for the third goal, the home side's best - and busiest -player was goalkeeper Randi Wardum. She made several fine saves and showed good handling to cut out crosses.
Scotland coach Anna Signeul said: "We played really well in the first half but our tempo dropped a bit in the second. It's easy for that to happen when you are so far ahead. It would also have been better if we'd kept a clean sheet but we have to be very happy coming to a place like this and winning so convincingly."
Rachel Corsie celebrated her 50th cap by heading Scotland into a seventh-minute lead from a Kim Little free kick. Another header, this time from Potsdam's Lisa Evans, doubled the advantage after 14 minutes. The cross was provided by Leanne Ross, who got the third goal when Wardum could not keep out her fierce shot from the edge of the box.
Jane Ross then ran in on goal to slip the ball past Wardum, and Leanne Ross made it five before the half-hour after a one-two between Leanne Crichton and Hayley Lauder.
The scoreline - with Faroese defender Rakul Johannesen being taken to hospital with a bad injury between the third and fourth goals - suggested a rout but the Scots had to wait for more than 30 minutes for their sixth, from Suzanne Lappin, two minutes after replacing her Glasgow City team-mate Crichton. The Scots' seventh came after 75 minutes, from substitute Suzanne Mulvey.
The Faroes still had enough resolve to score two quick goals, both from striker Heidi Sevdal, and they were loudly acclaimed by the home crowd.
In the other game in Group 4, favourites Sweden beat Poland 2-0 in Malmo on Saturday.