Russia and Poland have both won in qualifying to seal their places at the 2020 European Championship, while Netherlands and Germany both won to further their hopes.
Russia routed Cyprus 5-0 while Poland defeated North Macedonia 2-0 to join already qualified Belgium and Italy at next year's finals tournament.
Valencia forward Denis Cheryshev scored twice and set up two more for the Russians - who only needed a draw on Sunday to be sure of qualification - to take their tally to 21 points after seven wins from eight games in Group I.
With two games remaining, Russia have 11 points more than third-placed Cyprus and 12 more than fourth-placed Scotland, who thrashed San Marino 6-0 at a poorly attended Hampden Park in Glasgow.
Belgium already had their place at the finals secure but Roberto Martinez's team stayed perfect in qualifying with a 2-0 win over Kazakhstan in Astana.
Michy Batshuayi scored in the first half and Thomas Meunier wrapped up the win in the second, giving Belgium their eighth win from eight games.
The Belgians have scored 30 goals and conceded just one in their campaign.
"Everything is down to the focus of the players, this is an incredible group," Belgium coach Roberto Martinez said.
Second-half strikes from substitutes Przemyslaw Frankowski and Arkadiusz Milik guaranteed Poland will finish as one of the top two sides in Group G.
Leaders Poland have 19 points from eight matches, three clear of Austria who accounted for hosts Slovnia 1-0.
North Macedonia and Slovenia are on 11 points with all of the top four having two games to play.
Netherlands retained top spot in Group C with a 2-1 win over Belarus in Minsk, thanks to two first-half goals from Liverpool midfielder Georginio Wijnaldum.
Stanislav Dragun pulled Belarus back into the game but the Dutch held on to stay on course for qualification with 15 points from six matches.
They lead the group by virtue of their better head-to-head record over Germany, who survived a difficult first half and 14th-minute red card for Emre Can before a pair of deflected strikes from Ilkay Guendogan inspired a 3-0 victory over Estonia.
Guendogan's 51st and 57th minute efforts were reward for a positive start to the second half for the visitors while substitute Timo Werner added a 71st minute third.
"It was a hard bit of work. It was decisive that we lifted the pace in the second half," coach Joachim Loew told broadcaster RTL.
Northern Ireland are third, three points adrift, with two games remaining in November to settle the two qualifying spots.
Group E leaders Croatia missed the chance to secure their qualification as they drew 1-1 with Wales in Cardiff.
Nikola Vlasic gave Croatia a ninth minute lead before Gareth Bale replied for the hosts on halftime.
The result left 2018 World Cup runners-up Croatia on 14 points from seven games while Wales are on eight from six matches.
Mihaly Korhut's early strike gave Hungary a 1-0 win over Azerbaijan in Budapest to move them to second, on 12 points from seven games - two points clear of Slovakia who have a game in hand.
The top two teams of each of the 10 groups advance with the other four qualifiers to come through four tiers of playoffs.
Australian Associated Press