After Ireland's 2-1 win in Kazakhstan earlier, Germany topped Group C but wasted a chance to dominate their guests from the North Atlantic archipelago, who are ranked 152 places below the second-placed Germans according to FIFA.
Midfielder Mario Götze's first-half strike and Mesut Özil's brace after
the break ensured the hosts at least started the road to Brazil 2014 with three points.
Manchester City goalkeeper Gunnar Nielsen was the Faroe Islands' hero with a string of fine saves to frustrate the Germans five-man attack, which produced plenty of chances, but little finishing.
"It was clear to see from the beginning that we wanted to score, but our problem at the moment is we waste a lot of chances," admitted Germany coach Joachim Löw after the national team enjoyed the 500th win in their history. "Not only in this game have we needed a lot of opportunities to score."
"The Faroe Islands aren't the benchmark for other teams we will have to play in this group," added Löw, with Sweden, Austria and Ireland yet to come.
The Faroe Islands' Danish coach Lars Olsen admitted he was disappointed with the
two second-half goals his side conceded.
"The goalkeeper and the defence played well, but I have to say I am a little disappointed with the second-half goals, because we had spoken about the Germans being one of the best teams in the world for counter-attacks," he said.
"Ball possession was something like 85 percent for them to our 15, so I can only say I am satisfied with our performance."
With defensive midfielder Bastian Schweinsteiger left out as he recovers from injury, Löw changed to a 4-1-4-1 formation with Real Madrid's Sami Khedira playing behind a four-man attacking midfield with a single striker.
The experiment failed to impress as an uninspiring first-half saw Germany camp in the Faroe Islands' half with only the occasional foray from the guests when they looked to counter-attack on the break.
The breakthrough came in the 28th minute when Dortmund's Mario Gözte dribbled past the guests' defence and slammed his shot into the goal's bottom corner past Nielsen.
German captain Philipp Lahm epitomised his side's obvious frustration when he was booked for a yellow card after repeatedly pulling at midfielder Christian Holst before a sliding tackle in the 42nd minute.
Things improved after the break when Özil benefited from a good break down the right flank and converted Thomas Müller's cross on 54 minutes as Germany pulled clear.
Özil hit the third on 71 minutes after a good through-pass from Dortmund's Marco Reus put him into space in the penalty area with only Nielsen to beat.
Arsenal's Lukas Podolski came off the bench for the last 15 minutes for his 102nd cap, but squandered his single clear opportunity.
At the other end, Holst had the Islanders' best chance with a strike from 20 metres, which spurred Manuel Neuer into action after a quiet night in the German goal with eight minutes left.
Germany will play its next qualifier against Austria in Vienna on Tuesday, when Sweden entertains Kazakhstan. The Faroe Islands host Sweden on October 12.