The Germans have now made their best ever start to a World Cup qualifying campaign with four straight victories and no goals conceded.
German coach Joachim Loew, without more than six regulars including Jerome Boateng, Manuel Neuer and Toni Kroos, gave Werder Bremen winger Gnabry his first cap and he did not disappoint.
"The team tried to score goals and it was okay," Loew told reporters.
"Gnabry has shown, also for Werder Bremen, he is dangerous and he scored his goals tonight. He has a good run at the moment.
"We have said we want to dominate the entire qualification and we have succeeded so far," Loew added.
It was always likely to be a one-sided game as the world champions, second in the rankings, took on a team 199 places below them.
Sami Khedira opened the German account after seven minutes from an Ilkay Guendogan pass and Gnabry grabbed his first goal to double the lead in pouring rain.
The 21-year-old, joint top scorer and silver medallist at this year's Olympic Games, volleyed in his second early in the second half after full back Jonas Hector turned centre forward for Germany's third goal.
Hector scored again just past the hour as San Marino, consisting mainly of amateur players, ran out of steam. Gnabry completed a memorable debut for Germany by volleying in his third goal before a San Marino own goal in the 82nd.
"I did not count on scoring three goals on my debut," said Gnabry, who moved to Werder this season after failing to win a regular first-team place at Arsenal.
"I am very happy. The last two years were difficult but now I am playing many games and am in scoring form. I hope it will continue."
Substitute Kevin Volland added Germany's eighth five minutes from time.
The win lifted Germany to 12 points from four games at the top of Group C, having kept a clean sheet in every match.
It also gave Loew his 95th win as Germany coach, more than any other German manager, though he still trails Sepp Herberger in total matches in charge on 142 compared to 167.
(Reporting by Karolos Grohmann, editing by Ed Osmond)
