Coach Joachim Loew said his side had “done their duty” after their seventh win in eight Group C games left them on 22 points, five clear of Sweden, who beat Kazakhstan earlier in the day.
Per Mertesacker gave the Germany a 1-0 halftime lead although they had to wait until the last 20 minutes for further goals when Mesut Ozil converted a penalty won by Thomas Mueller, who scored the third goal himself.
The hosts had Atli Gregersen sent off for the foul which led to the penalty.
“It was our duty to get the three points and we did it,” Loew told German television, looking distinctly unenthusiastic.
“We saw that the Faroes can defend well. It was not easy to come through. We must especially improve our final pass and our finishing,” added the coach, who had suggested in March that teams such as the Faroes should take part in a preliminary competition rather than go straight into the group stage.
The Germans next host Ireland before finishing off away to Sweden and need two points from the two games to guarantee top spot.
Like many other teams before them, Germany found the Faroese part-timers to be a tough proposition on home ground. They were made to battle for their points although there was never any doubt about the outcome.
Germany goalkeeper Manuel Neuer was called into action early on when he had to turn over a shot by Pol Johannus Justinussen. Julian Draxler and Miroslav Klose had already struck the woodwork for the visitors when Mertesacker opened the scoring in the 23rd minute.
The Arsenal defender sidefooted in from close range after Jerome Boateng flicked on a corner at the near post.
Germany predictably dominated the match but created surprisingly few chances as the hosts defended doggedly.
They finally made the game safe when Mueller was tripped as he raced in on goal and Ozil sent Gunnar Nielson the wrong way.
Mueller then fired in the third with six minutes left, completing the Faroes’ eighth straight defeat in the group.
Germany’s players sounded just as uninspired as their coach by the workmanlike win.
“It’s a mental thing,” said forward Miroslav Klose. “When you switch on to the fact that you have the better players and better team, you win this sort of match.”
Mueller added: “We have completed our task, so we are going home satisfied.”
(Reporting by Brian Homewood in Berne, editing by Mitch Phillips)