Florian Kamberi hit a hat-trick for Neil Lennon's side and Stevie Mallan grabbed a double. Oli Shaw was also on target against the team from the Faroe Islands, who finished with 10 men.
Rangers take a 2-0 lead to Macedonia next week after goals from Jamie Murphy and James Tavernier (penalty) saw off FK Shkupi in Steven Gerrard's first competitive game in charge.
