Thomas Muller was on target twice while Joshua Kimmich’s first goal for his country crowned an emphatic start to qualifying for Germany, who immediately took their place at the top of Group C.
Ruslan Gurbanov’s goal just before half-time saw Azerbaijan get their campaign off to a winning start with a 1-0 victory over 10-man San Marino, who had Cristian Brolli sent off early in the second half, and the Czech Republic drew 0-0 with Northern Ireland.
Denmark were the only team to make a winning start in Group E thanks to Christian Eriksen’s first-half strike against Armenia in Copenhagen, as Kazakhstan and Poland shared a 2-2 draw while Romania and Montenegro shared the points in a 1-1 draw.
Bartosz Kapustka’s strike and a Robert Lewandowski penalty had Poland in control but a quick-fire double from Sergei Khizhnichenko early in the second half earned an impressive 2-2 draw for the hosts.
Late drama in Romania saw Stevan Jovetic’s 87th-minute header cancel out Adrian Popa’s goal for the hosts just two minutes previously, before Nicolae Stanciu put a penalty over the crossbar in the seventh minute of injury time.
Adam Lallana ensured Sam Allardyce’s reign as England manager got off to a dramatic winning start with a strike deep into injury time against Slovakia.
Also in Group F alongside England, Scotland made a winning start as a hat-trick from Hull’s Robert Snodgrass helped secure a 5-1 victory in Malta.
Snodgrass’ over-hit cross flew into the far top corner to give Gordon Strachan’s side a ninth-minute lead but Alfred Effiong quickly headed an equaliser.
Chris Martin restored Scotland’s lead just after half-time before a harsh red card for home defender Jonathan Caruana. Snodgrass scored from the resulting penalty and a Steven Fletcher header extended the lead.
Snodgrass tapped in for his hat-trick after a Fletcher shot had struck the crossbar, and Malta finished with nine men after Luke Gambin was sent off for a hack at Snodgrass.
The other game in Group F saw Slovenia fight back from two goals down to draw in Lithuania. Quick-fire goals from Fedor Cernych and Vykintas Slivka had the hosts in control at half-time but headed goals from Rene Krhin and Bostjan Cesar – the latter in injury time – earned Slovenia a point.