Slovakia hammered Cyprus 6-1 in Group D, whilst Germany and Czech Republic also opened their campaigns with three points.
In Bratislava, Slovakia ran rampant against Cyprus, scoring three goals in each half in a thumping home win.
Martin Skrtel set them on their way after nine minutes as he converted a cross from Marek Mintal, and the provider then became the poacher as the striker grabbed a brace (33, 56).
Rangers new-boy Filip Sebo scored either side of half time (43, 49), whilst Miroslav Karhan also contributed (52), as Slovakia raced into a six-goal lead before the hour mark.
However, Cyprus restored some pride when Giasemis Giasemi scored in injury time.
Slovakia were joined at the top of Group D by Germany and Czech Republic, who triumphed over Republic of Ireland and Wales respectively.