Despite missing national number one Alexander Zverev in Dusseldorf, Germany held an overnight 2-0 lead in the tie thanks to Yannick Hanfmann and Jan-Lennard Struff.
The doubles duo of Kevin Krawietz and Tim Puetz wrapped up Germany's spot in round two of qualifying with a 6-0, 2-6, 6-4 over Ignacio Buse and Arklon Huertas del Pino.
World number 196 Justin Engel, aged 18, then defeated Gonzalo Bueno 6-3, 6-7(4), retired with the final singles tie not being played.
Dino Prizmic secured the decisive win 7-6(5), 7-6(2) against Elmer Moller as Croatia bested Denmark 3-1.
With play restarting in Varazdin locked at 1-1 overnight, Nikola Mektic and Mate Pavic eased to a 6-2, 7-5 win over Johannes Ingildsen and Carl Emil Overbeck to set up the win for the hosts.
Austria edged a tight encounter with Japan in Tokyo, 3-2, thanks to a clutch 5-7, 6-1, 6-0 victory for 170th-ranked Jurij Rodionov against former world number 24 Yoshihito Nishioka.
"It's a team competition," Rodionov said. "Everyone has to do their part and I'm happy I was able to get the two points for my team and decide the tie for Austria."
USA lead hosts Hungary 2-0 ahead of Sunday's deciding three matches courtesy of a straight-sets win for Tommy Paul over Zsombor Piros, before Ethan Quinn thrillingly beat Fabian Marozsan 6-3, 3-6, 7-6(11).
Elsewhere, France are locked 1-1 with Slovakia and Belgium lead Bulgaria 2-0.
The winner of the France-Slovakia tie will face Canada, who won the last two singles matches on Saturday to beat Brazil 3-2.
The teams had finished day one in Vancouver tied at 1-1. Brazil won Saturday's doubles but Canada rallied as Gabriel Diallo beat Matheus Pucinelli De Almeida 3-6, 6-1, 7-6(4) and Liam Draxl beat Gustavo Heide 6-3, 6-4.