Germany flexed its muscle with an 8-0 rout of Estonia, Italy scored a late winner to beat Bosnia-Herzegovina 2-1 and Belgium eased to a 3-0 win over Scotland.
France, which lost 2-0 in Turkey on Saturday, recorded a 4-0 win over tiny Andorra.
Russia, which thrashed San Marino 9-0 on Saturday for its biggest win since the Soviet era, had to settle for a 1-0 win at home over Cyprus.
Here's a look at Tuesday's games:
GERMANY RAMPANT
Germany's rout of Estonia capped a good week for interim coach Markus Sorg, who took charge of the side for two games while Joachim Löw recovers from an injury he sustained in the gym.
Marco Reus and Serge Gnabry both scored twice, while Leon Goretzka, Ilkay Gündogan, Timo Werner and Leroy Sané added the other goals.
Reus opened the scoring in the 10th minute before Gnabry, Goretzka and a penalty from Gündogan had Germany four goals up inside the first 26 minutes — for the first time since its 7-1 win over Brazil in the 2014 World Cup semifinals.
Despite its third win from three games, Germany is behind Northern Ireland, which stayed perfect thanks to Paddy McNair's late goal for a 1-0 win in Belarus.
Germany next plays the Netherlands in September.
ITALY RALLIES
Marco Verratti scored Italy's late winner against Bosnia-Herzegovina to keep the Azzuri top of Group J, three points clear of second-place Finland, which won 2-0 in Liechtenstein. Armenia is third, six points behind Italy, after stunning Greece 3-2 in Athens.
Edin Dzeko's first-half opener for Bosnia was the first goal Italy has conceded in its four qualifying matches.
BELGIUM DOMINATES
New Real Madrid signing Eden Hazard led Belgium to another win, setting up Romelu Lukaku for the team's opener after he had combined with his brother Thorgan.
Lukaku grabbed his second after the break before Kevin de Bruyne sealed the win late.
Scotland keeper David Marshall helped keep the score down for the visitors.
Belgium leads Group I with 12 points, three more than Russia and six more than both Kazakhstan and Scotland.
FRANCE RECOVERS
France, which also scored four goals in each of its first two wins in Group H, got back on track after its loss in Turkey.
Star forward Kylian Mbappé got the visitors off the mark before Wissam Ben Yedder, Florian Thauvin and Kurt Zouma each got their first international goals for France.
"We reacted well after not playing to our usual level on Saturday," France coach Didier Deschamps said. "I think the players enjoyed themselves."
Iceland upset Turkey with a 2-1 win. The Turkish team had complained that it was delayed at Keflavik Airport on Sunday while officials searched bags at a slow pace.
HUNGARY IN CONTENTION
Hungary defeated Wales 1-0 at home to open a three-point lead over Croatia and Slovakia in Group E. Hungary has played a game more, however.
Marek Hamsík became Slovakia's all-time top scorer with two goals in the side's 5-1 win in Azerbaijan.