Florian Wirtz starred on Thursday (Friday AEST) as Germany defeated Serbia 2-0 in Munich for Klopp's first win at the third attempt — staving off an unwanted record.
"We played great ... I am really happy. This performance must now be the baseline," Klopp said.
The former Liverpool boss was on the verge of becoming the first Germany coach not to win any of his first three games after opening with a 1-1 draw with the Netherlands last week before Sunday's shock 1-0 defeat to Greece.
Derry Scherhant, Nick Woltemade and Serge Gnabry all missed good chances for the hosts before Tom Bischof broke the deadlock in the 39th minute on the rebound after Wirtz struck the post.
Cologne star Said El Mala debuted along with Bayern goalkeeper Jonas Urbig and Freiburg forward Scherhant, but it was Wirtz who made it 2-0 after taking a cross past a defender with his first touch and sending it inside the right post with his next.
In Thessaloniki, Tijjani Reijnders scored late as the Dutch fought back to draw 2-2 with Group A2 leaders Greece.
Fotis Ioannidis scored one goal and set up the other for Giorgos Masouras. Virgil van Dijk netted before the hour mark and Reijnders equalised in the 89th.
Joao Felix sealed Portugal's 4-2 win over Denmark in Copenhagen, where the visitors were without Ronaldo after he walked out on the team the day before after an apparent rift with coach Jorge Jesus.
Goncalo Ramos, who has taken the 41-year-old forward's place, set up Joao Cancelo's opener, then responded with Portugal's second goal two minutes after Mikkel Damsgaard equalised in the 23rd.
Rasmus Hojlund drew the Danes level again in the 53rd. Vitinha restored Portugal's lead with a near-post header to Bruno Fernandes' free kick in the 67th and Felix made sure of the win in the 87th.
Wales got their first victory after beating 10-man Norway 2-1 in Cardiff - also in Group A4.
In Group B3, Austria fought back from 2-0 down to draw 2-2 with the Republic of Ireland in Dublin – where there had been stoppages during the first half following protests in support of Palestine.
Elsewhere, Israel and Kosovo played out a 0-0 draw, Malta and Gibraltar drew 1-1 and Azerbaijan were held to a goalless draw by Liechtenstein.
With PA & Reuters.
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