Soldado's 86th-minute winner saved Spain from an embarrassing stalemate in Tbilisi in the opening match of their Group I challenge.
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.
France top Group I after making it two wins out of two with a 3-1 triumph over Belarus at the Stade de France.
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 promptly scored, 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.
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 in Modena.
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 home 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.
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