The reigning world champions secured a ninth straight win in qualifying on Thursday to guarantee they will finish top of Group C and play at the showpiece tournament for the 19th time in their history.
Bayern Munich midfielder Sebastian Rudy gave Germany a superb start with a long-range strike inside two minutes before former Hoffenheim team-mate Sandro Wagner added a second goal in the 21st minute.
Joshua Kimmich volleyed in a third in the closing minutes and although Northern Ireland found the net in injury time through Josh Magennis, Low refused to let conceding at the death dampen his mood.
"I am satisfied," Low told reporters afterwards in Belfast.
"We doubled the lead very quickly. In the Czech Republic we took the lead early too but then lost control. That did not happen today.
"We felt on the pitch that we had everything under control in the second half. That's when we slowed down a little bit."
Rudy's stunning opener was crucial against a Northern Ireland side who had not conceded a goal in qualifying since losing the reverse fixture 2-0 in Hannover last October.
The 27-year-old's effort – his first in international football – put Germany on their way to Russia - and now they can focus on retaining the World Cup.
"The goal was extremely important. We dominated the match the whole time," Rudy said.
"We're going to Russia to win something. We want to defend the title."