Wales started with a tense win over Slovakia, while Belgium and Poland enjoyed comfortable victories over Cyprus and Latvia.
• Facing old rivals the Netherlands for the third time in six months, Germany enjoyed their revenge.
The Dutch beat Germany 3-0 in Amsterdam in October and earned a last-gasp draw in the return fixture.
Those results helped relegate Germany from the top tier of the Nations League — further embarrassment after their abysmal 2018 World Cup campaign.
Schulz's winner came just when it looked like his team had let the Dutch salvage a draw from 2-0 down.
"We didn't control the ball, and if you can't exert pressure, the game opens up, and you see they have some amazing attackers," Netherlands coach Ronald Koeman said.
Germany had gone six competitive games without a win since beating Sweden at the World Cup.
The challenge now for Loew is to keep the momentum going — after all, the win over Sweden was seen at the time as a much-needed boost after a poor run. It proved a false dawn when Germany lost to South Korea and crashed out of the World Cup.
Germany's next opponents, Belarus, lost 2-1 to group leaders Northern Ireland who won their second straight game with an 87th-minute goal from substitute Josh Magennis.
• Eight months after reaching the World Cup final, Croatia are unexpectedly struggling. Croatia's defence was at times overwhelmed by a spirited Hungary team, conceding one goal to a fine passing move masterminded by Balazs Dzsudzsak and the other after poor set-piece defending.
Since losing the World Cup final to France, Croatia's results have been wildly inconsistent. A 6-0 loss to Spain in the Nations League, a 3-2 win over Spain soon after and Friday's laboured 2-1 win over Azerbaijan have highlighted Croatia's moments of brilliance and vulnerabilities after losing key players to international retirement and injury.
Earlier in the same group, Daniel James' first international goal gave Wales the lead after five minutes against Slovakia before holding on to win 1-0.
"It was a perfect start," Wales coach Ryan Giggs said, and he was full of praise for 21-year-old James. "He is a talent, and when you've got that raw pace, you're a threat at any level."
• One hundred games for Belgium and Eden Hazard is still dangerous.
Hazard scored his 30th career international goal in his centenary game as Belgium beat Cyprus 2-0. Michy Batshuayi finished with a goal and an assist as Belgium eased to a routine win to top their group with six points.
Valencia winger Denis Cheryshev scored two goals and set up another as Russia bounced back from their opening loss to Belgium on Friday with a 4-0 dismantling of Kazakhstan.
Still mourning last week's loss to Kazakhstan, Scotland fans had little to celebrate as their team struggled to a 2-0 win over San Marino, the world's lowest-ranked team.
Scotland, who haven't qualified for a European Championship since 1996, are still guaranteed a playoff spot thanks to Nations League results.
- AP
