Record-breaking Poland striker Robert Lewandowski scored a hat-trick in a 6-1 win over Armenia on his way to becoming his country's all-time leading scorer.
Within the space of seven first-half minutes in Yerevan, the Bayern Munich forward equalled and then surpassed Wlodzimierz Lubanski's tally of 48 before reaching a half-century for his country when he completed his treble midway through the second half.
His 64th-minute strike was his 15th in Group E, a new record for a single European qualifying campaign, although Portugal's Cristiano Ronaldo is hot on his heels with 14.
Kamil Grosicki, Jakub Blaszczykowski and Rafal Wolski scored the others to put Poland on the verge of World Cup qualification, with Hovhannes Hambardzumyan briefly making it 3-1 just before the break.
Denmark's 1-0 win over Montenegro, courtesy of Tottenham forward Christian Eriksen's 16th-minute goal, means Poland need a point against the Montenegrins on Sunday to secure their spot for Russia next year.
Two first-half goals in quick succession by Constantin Budescu teed up a 3-1 win for Romania with Claudiu Keseru adding the third before Kazakhstan's Bauyrzhan Turysbek pulled one back late on.
World champions Germany booked their place with a 3-1 win over nearest-challengers Northern Ireland in Group C.
A stunning strike from Sebastian Rudy in only the second minute set the tone for a comfortable victory which saw Sandro Wagner double their lead in the first half, before Joshua Kimmich wrapped up three points just before the end with Josh Magennis' added-time header a consolation for the hosts.
Elsewhere in the group Jan Kopic and Antonin Barak scored the Czech Republic's goals in a 2-1 win in Azerbaijan, for whom Afran Ismayilov equalised from the penalty spot.
Norway hammered San Marino 8-0 with Mohmed el Younoussi scoring a hat-trick, Josh King getting two and Markus Henriksen, Ole Selnaes and Martin Linnes also on target.
In Group F England qualified as a late Harry Kane goal gave them a 1-0 win at home to Slovenia, while Scotland kept alive their hopes of securing a play-off place by beating main rivals Slovakia by the same scoreline, courtesy of Martin Skrtel's own goal, to move them into second place in the group.
Malta were consigned to finish last in the group despite securing their first point of the campaign with a 1-1 draw at home to Lithuania which saw the islanders' Andrei Agius have his opener cancelled out by Vykintas Slivka.