Thomas Mueller scored twice for the second straight World Cup qualifier to lead Germany to a comprehensive 3-0 win over Czech Republic in Group C.
Toni Kroos hit the other as the world champions now have six points from two games.
Azerbaijan beat Norway 1-0 to also maintain their perfect start to the qualifying campaign.
Northern Ireland thrashed San Marino 4-0 to sit third in the group on four points.
Bayern Munich striker Robert Lewandowski notched up a hat-trick of goals as Poland edged past Denmark 3-2 at the National Stadium in Warsaw.
The result leaves Adam Nawalka’s men on four points from their opening two Group E games – level with Montenegro and Romania.
Montenegro and Romania kept pace with Poland, both registering 5-0 victories over Kazakhstan and Armenia respectively.
Gareth Southgate began his stint in charge of England with a 2-0 win over minnows Malta in Group F at Wembley.
Daniel Sturridge headed home the opener while Dele Ali put the game to bed just before half time.
The three Lions could have won by a bigger margin had it not been for an heroic performance by Malta goalkeeper Andrew Hogg.
England have now won their last 14 qualifying games and are unbeaten in their last 31 qualifiers overall (won 24, drawn 7).
England have a perfect six points and top the group two points clear of Scotland who drew 1-1 with Lithuania.
Elsewhere Slovenia defeated Slovakia 1-0.