France, Portugal and Italy enjoyed comfortable wins, while Joachim Low bemoaned his side's lack of edge as they beat Austria 2-1.
World Cup qualifying round-up: Champions Spain toil against Georgia
Roberto Soldado's 86th-minute winner saved Spain from an embarrassing goalless draw with Georgia in the opening match of their World Cup qualifying campaign.
The Valencia striker, starting for the world champions ahead of Cesc Fabregas and Fernando Torres, swept the ball home following a short corner to spare the visitors' blushes.
Soldado was the only change to the side that started the Euro 2012 final victory over Italy, but Vicente del Bosque's side were far from at their slick best and almost went behind when Alexander Amisulashvili struck a post.
Afterwards, Del Bosque hailed Georgia's 'extraordinary' performance.
"They put us in a lot of difficulty with their enthusiasm and their ability to defend all our attacks through both the centre and the wings," he said.
"We knew they would be organised, defend well and that they have options up front with strength that we had to be careful of. It wasn't through courtesy that I spoke about them being a strong rival beforehand.
"The differences in football are getting smaller every day. We have to play a qualification campaign and we can't think about anything other than just qualifying."
France topped Spain's Group I after making it two wins out of two with a 3-1 triumph over Belarus.
Etienne Capoue put Didier Deschamps side in front early in the second half and Christophe Jallet added a second.
Les Bleus had a scare when Sergey Kornilenko missed a penalty and Anton Putsila did score a minute later, but Franck Ribery settled the nerves 10 minutes from time.
Germany continued their 100% start to Group C with a 2-1 win in Austria.
Goals from Marco Reus and a Mesut Ozil penalty either side of half-time had Joachim Low's side in control, Zlatko Junuzovic pulling one back for the hosts, though afterwards coach Joachim Low felt his side should have won a larger margin.
"We had the chances to make it 3-0, which we should have done," he said.
"They showed a lot of energy but they tired after an hour or 70 minutes and we should have got the third goal and that would have been that.
"Instead, we let them come at us and committed too many mistakes."
Sweden won their opening game 2-0 at home to Kazakhstan, Rasmus Elm and Marcus Berg on target.
Italy got their first win in Group B with a 2-0 success over Malta.
After a 2-2 draw with Bulgaria in their opener, goals at either end of the match from Mattia Destro and Federico Peluso gave the hosts three points.
Bulgaria joined them on four points after a bad-tempered 1-0 win over Armenia.
Stanislav Manolev scored the winner, but the highlight of the second half was a flurry of red cards, Bulgaria's Svetoslav Dyakov and Armenia's Marcos Pizelli and Gevorg Ghazaryan all sent off.
Holland, so poor in the European Championship, won 4-1 in Hungary to get their second win in Group D.
Jeremain Lens' early opener was quickly cancelled out by a penalty from Balazs Dzsudzsak, but Bruno Martins Indi scored to give the Dutch a 2-1 half-time lead.
Lens with his second and Klaas Jan Huntelaar struck it the second half to ensure a convincing win.
Romania joined them on top of the group after a 4-0 win at home to Andorra, Gabriel Torje, Costin Lazar, Valerica Gaman and Alexandru Maxim on target.
Turkey were 3-0 winners over 10-man Estonia, the goals from Emre Belozoglu, Umut Bulut and Selcuk Inan. Enar Jaager was sent off for the visitors after 19 minutes.
Poland and Montenegro joined England on top of Group H with four points.
The Poles saw off Moldova 2-0 thanks to a Jakub Blaszczykowski penalty and a Jakub Wawrzyniak strike.
Montenegro hit minnows San Marino for six, with two goals each from Fatos Beqiraj and Andrija Delibasic and one apiece for Luka Djordjevic and Elsad Zverotic.
Portugal and Russia established a five-point cushion over the chasing pack in Group F.
Portugal recorded their second win of the campaign, 3-0 against Azerbaijan, courtesy of second-half efforts from Silvestre Varela, Helder Postiga and Bruno Alves, the last two coming in the final five minutes.
Russia found the going rather easier in Israel, an Alexander Kerzhakov double and goals from Aleksandr Kokorin and Viktor Faitzulin giving them a 4-0 win.
In Group A Belgium and Croatia joined Serbia on top of the pile after a 1-1 draw, Guillaume Gillet cancelling out Ivan Perisic's opener.
Switzerland continued to lead the way in Group E, Xherdan Shaqiri and a Gokhan Inler penalty giving them a 2-0 home win over Albania.
Konstantinos Makridis scored to give Cyprus a 1-0 win over Iceland, who had Solvi Ottesen sent off late on.
Norway fought back to defeat Slovenia 2-1, John Arne Riise getting the winner with a 90th-minute penalty.
Markus Henriksen cancelled out Marko Suler's opener.
Bosnia-Herzegovina and Greece won for the second time in Group G.
The former crushed Latvia 4-1, but only after conceding a Kaspars Gorkss' goal after five minutes.
Zvjezdan Misimovic scored twice, including a penalty, while Miralem Pjanic and Edin Dzeko got one each as the hosts recovered.
Greece beat Lithuania 2-0 thanks to goals from Sotiris Ninis and Kostas Mitroglou.
Slovakia recorded a 2-0 win over Liechtenstein, Marek Sapara and Martin Jakubko on target.
The USA got their qualifying campaign back on track with a 1-0 win over Jamaica in Ohio.
Herculez Gomez scored from a second half free kick to avenge last week's shock defeat by the Jamaicans and move the US level with Jamaica and Guatemala in Group A.
Guatemala defeated Antigua and Barbuda 1-0, Venezuela beat Paraguay 2-0 and El Salvador edged Guyana 3-2.