Bosnia-Herzegovina put eight past Liechtenstein, Greece overcame Latvia 2-1 and Slovakia held Lithuania to a 1-1 draw.
Edin Dzeko and Vedad Ibisevic scored a hat-trick apiece as Bosnia-Herzegovina thrashed Liechtenstein 8-1 in their opening match.
Bosnia-Herzegovina midfielder Zvjezdan Misimovic scored twice in five minutes before Ibisevic netted two goals as the visitors took a comfortable four-goal lead at half-time.
Their domination continued after the break when Manchester City forward Dzeko fired a hat-trick before strike partner Ibisevic sealed his own three-goal effort from the six-yard box with seven minutes left on the clock.
Substitute striker Mathias Christen at least ensured Liechtenstein got on the scoresheet in the 61st minute, scoring at the second attempt after Bosnia-Herzegovina and Stoke goalkeeper Asmir Begovic failed to block his initial shot.
Greece came from behind to secure all three points in Latvia and get off to a winning start on the long road to Brazil.
The visitors fell behind when Aleksandrs Cauna converted a 43rd minute penalty, but bounced back after the break with strikes from Nikos Spyropoulos (57) and Theofanis Gekas (70).
Lithuania and Slovakia came away with a point apiece from their clash in Vilnius after both being reduced to 10 men.
The home side went 1-0 up in the 18th minute through Marius Zaliukas before Marek Sapara's 41st minute leveller.
Slovakia striker Viktor Pecovsky was shown a straight red card early in the second half, but Lithuania failed to take advantage and had substitute Tadas Labukas dismissed for a second bookable offence in stoppage time.