David Hancko put the hosts in front shortly before half-time.
Middlesbrough forward David Strelec curled home a fine second goal after 55 minutes to leave Germany boss Julian Nagelsmann’s facing more questions over his squad.
Northern Ireland battled to a 3-1 win away against 10-man Luxembourg.
Jamie Reid gave the visitors an early lead when he slotted in after Isaac Price’s penalty had been saved, but Augsburg winger Aiman Dardari equalised on the half-hour for his first senior international goal.
Shea Charles struck straight after the break before Luxembourg defender Seid Korac was sent off just after the hour for a second caution. Crystal Palace midfielder Justin Devenny then wrapped things up with 20 minutes left.
European champions Spain coasted to a 3-0 win in their Group E opener away to Bulgaria.
La Roja took an early lead to dampen a partisan capacity home crowd at the Vasil Levski National Stadium when Mikel Oyarzabal struck after just five minutes.
Chelsea wing-back Marc Cucurella drilled home a second on the half-hour before Arsenal midfielder Mikel Merino headed in a third from a corner to put the Nations League runners-up in control.
Turkey had earlier won 3-2 in Georgia, where they finished with 10 men.
Mert Muldur’s header gave the visitors a third-minute lead with Kerem Akturkoglu then striking twice either side of the break.
Zuriko Davitashvili pulled a goal back just after the hour before tempers flared in the 71st minute.
Turkey substitute Baris Alper Yilmaz was shown a red card for a late challenge on Giorgi Kochorashvili – with Georgia manager Willy Sangol then sent from the dugout for his protests.
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Spain’s Marc Cucurella celebrates scoring their second goal with Martin Zubimendi and Nico Williams REUTERS/Stoyan Nenov
Khvicha Kvaratskhelia struck a late second for Georgia deep into added time.
Aston Villa defender Matty Cash fired in a late equaliser as Poland fought back to draw 1-1 with the Netherlands in Rotterdam.
Denzel Dumfries headed the Oranje – who had won their opening two games – in front from a 28th minute corner.
Cash, though, secured a point when he drilled an angled shot into the top corner with 10 minutes left.
Lithuania scored a stoppage-time penalty to snatch a 1-1 draw with Malta in Kaunas – where both sides had a player sent off during a chaotic ending.
Wales went top of Group J with a hard-fought 1-0 win away to Kazakhstan in Astana.
Kieffer Moore marked his 50th cap with a 24th-minute goal as Wales held out after Kazakhstan twice hit the crossbar during the second half.
Belgium later thrashed Liechtenstein 6-0 to make it two wins from their three games so far.
Maxim De Cuyper’s header set Belgium on their way in the first half. Youri Tielemans scored twice after the break while Arthur Theate, Kevin De Bruyne and Malick Fofana were also on target.