Germany routed Austria 6-2 to become the first team to qualify for Euro 2012.
Top-ranked Netherlands routed San Marino 11-0 in its biggest win to move a step closer to the finals on Friday.
Real Madrid playmaker Mesut Oezil's two goals and further scored by Miroslav Klose, Lukas Podolski, Andre Schurrle and Mario Gotze sealed the free-scoring Germans' eighth straight win in qualifying, giving them an insurmountable lead in Group A.
The Dutch are on the brink of joining them in the field in Ukraine and Poland. Arsenal striker Robin van Persie's four-goal haul and two each from Wesley Sneijder and Klaas Jan Huntelaar preserved the team's perfect record and pulled it six points ahead in Group E.
Two more European heavyweights also moved into strong positions to secure qualification. Wayne Rooney scored twice in England's 3-0 victory at Bulgaria, and Italy squeezed past Faeroe Islands 1-0 thanks to Antonio Cassano's early strike.
With closest rival Montenegro losing 2-1 at Wales, England is three points clear in Group G with two matches remaining. The Italians require just one win from their last three games to take Group C.
Elsewhere, France went three points clear in Group D with a 2-1 win in Albania, and Real Madrid forward Cristiano Ronaldo scored twice as Portugal beat Cyprus 4-0 to stay first in Group H, tied in points with Norway.
With Turkey getting an injury-time winner to beat Kazakhstan 2-1 and grab second place, Germany had to beat Austria to guarantee advancement.
Klose gave the hosts the perfect start, his 62nd international goal opening the scoring. Oezil, back in his hometown of Gelsenkirchen, then took center stage by netting twice around Podolski's goal.
Elsewhere in the group, Belgium drew 1-1 at Azerbaijan and is a point behind Turkey while having played one more game.
The Netherlands celebrated climbing above Spain in the world rankings last week by demolishing San Marino and could join Germany in the finals with a victory over Finland on Tuesday.
"It's not the toughest opponent around," Netherlands coach Bert van Marwijk said of San Marino, which is tied for last in the rankings.
Gergely Rudolf scored a last-minute winner as Hungary beat Sweden 2-1 to move even with its opponent on 15 points. Sweden is ahead on goal difference and has played one game fewer.
Slovenia, which lost 2-1 to Estonia, stayed second to Italy but is now level in points with Serbia, which won 1-0 at Northern Ireland on Marko Pantelic's second-half goal.
Karim Benzema and Yann M'Vila were the scorers for France, which held on after Albania forward Erjon Bogdani halved the deficit in the 46th minute.
Bosnia-Herzegovina is now the closest challenger to the French after a 2-0 win at Belarus.
Group H is likely to go down to the wire after Portugal followed Norway's 1-0 success against Iceland with a romp in Cyprus, Hugo Almeida and Danny adding to Ronaldo's goals.
Russia took advantage of Ireland's 0-0 draw at home with Slovakia by moving two points clear of the pair in Group B with a 1-0 victory over Macedonia. Igor Semshov got the 41st-minute winner.
Greece and Croatia look set to battle for the top spot in Group F with three matches still remaining after grabbing away victories.
The Croatians were comfortable 3-1 winners at Malta, but remain a point behind Greece, which eked out a 1-0 win at third-place Israel on Sotorios Ninis' goal.
In World Cup play, Australia and Japan needed late goals to win qualifying games in Asia. Park Chu-young had a hat trick for South Korea in a 6-0 rout of Lebanon. China and Uzbekistan also won as the group stage third round began, involving the region's major teams for the first time.