But Sweden poured in three goals against them in the second half, not only putting themselves atop the group, but putting Mexico in danger of missing out on advancing altogether.
Being a defending champion at the World Cup has proven to be a tough challenge in recent years.
South Korea and Germany both finished Group F with one win and two losses, but the Taeguk Warriors had edge on goal difference to finish third. "We tried hard to win, but we never earned the chance to take the lead".
Instead, Low favored Bayer Leverkusen's Julian Brandt - although the 22-year-old made just one appearance from the bench in Russian Federation, coming on with around 10 minutes to play in the final ill-fated game against South Korea.
Coming off a 1998 triumph on home soil, Les Bleus were one of the favourites for the Japan/South Korea World Cup four years later.
South Korean media hailed the win over the world's top-ranked side as the "Miracle of Kazan" after defeat at the hands of Germany in 2002 in Seoul.More news: Russian Embassy condemns attempt on Zimbabwe president's life
But Sweden's 3-0 win against the Mexicans meant Germany desperately needed another injury-time victor to progress against South Korea.
The World Champions - or the ex-World Champions as they are now known - went down 2-0 to the previously winless South Koreans and will exit the tournament at the first hurdle for the first time since 1938.
Low has been coaching Germany since 2006, when he took over for Jurgen Klinsmann.
In Spain, meanwhile, national sport newspaper Marca called Germany's exit "the curse of the champions". South Korea switched 4-1-4-1 when defending, but the skillful Mexicans knew how to exploit open space and dominate the midfield.
It was the end of an era for the likes of Iker Casillas, Xavi Hernandez and Xabi Alonso.
So, by all means soak up the schadenfreude, but don't expect it to last for too long.