Croatia took the early initiative in Group D as they saw off Nigeria 2-0 in their World Cup opener at the Kaliningrad Stadium.
With Iceland having held Argentina to a 1-1 draw earlier on Saturday, Croatia took full advantage.
An own goal from Oghenekaro Etebo, set to play at Stoke next season, broke the deadlock just after the hour, with a penalty from captain Luca Modric with 20 minutes left securing three points for Zlatko Dalic's men.
Croatia had the better of the opening exchanges, with Andrej Kramaric's long-range effort drifting wide of the right-hand post.
The deadlock was broken in the 32nd minute in somewhat fortunate circumstances.
Modric's corner was flicked on by Ante Rebic. Mario Mandzukic's tame diving header looked to be going wide, before the ball was deflected in off midfielder Etebo.
Croatia, though, welcomed their slice of good fortune - and almost added a second just before half-time when Kramaric's header dropped onto the roof of the net.
The Super Eagles, who played England in a warm-up match at Wembley, regrouped at the interval.
Mandzukic was in the right place in his own penalty area to block Leon Balogun as the defender aimed to head in from a corner.
Chelsea midfielder Victor Moses then fired a low shot wide at the near post.
Croatia should have doubled their lead in the 56th minute, when Ivan Perisic whipped the ball across the Nigeria penalty area from the left channel, only for Eintracht Frankfurt winger Ante Rebic to send his close-range volley wide.
Moses claimed for a penalty when he went down in a heap under a challenge from Ivan Strinic, but Brazilan referee Sandro Ricci waved away the appeal.
With 20 minutes left, Croatia were awarded a spot-kick after Mandzukic was man-handled by Bursaspor defender William Troost-Ekong at a corner.
Modric made no mistake with the penalty, sending goalkeeper Francis Uzoho the wrong way as the Real Madrid midfielder tucked the ball into the bottom left corner.