Croatia, who were barely extended by their African opponents, now top Group D after Argentina and Iceland drew 1-1 in Moscow earlier on Saturday.
Oghenekaro Etebo was helpless in deflecting the ball into his own net in the 32nd minute and a second half spot-kick from Real Madrid star Modric sealed the points. "If we do exactly what we know we can do, to control the game and be aggressive, we can do well", said Rohr.
Just three days into the World Cup, the scrappy goal added to what is becoming a pattern, following a Moroccan own goal that handed victory to Iran on Friday and a deflected Paul Pogba effort that earned France a 2-1 win over Australia earlier on Saturday.
The last time Croatia won their opening group game was back in 1998, and coach Zlatko Dalic said he was glad the squad had put that unfortunate record behind them. "We told them it is impossible".
The Super Eagles of Nigeria got off to a disappointing start at the 2018 Federation Internationale de Football Association world cup as they lost to their Croatian counterparts by two goals to nil.
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Just after the half-hour mark, Mandzukic, industrious in his hold-up play, chested a Andrej Kramaric cross back to Ante Rebic, whose fizzing shot was blocked.
In Russia's sleepy European exclave of Kaliningrad - perhaps best known for its nuclear missile sites - the much-hyped youngsters of Nigeria struggled to ignite against Croatia's midfield technicians. The resulting corner saw Rebic return the favour with a near-post flick on met by a diving Mandzukic. "We feel ready, we have prepared really well and it's a game we want to win to start the tournament well".
In the 69th minute Croatia got their insurance goal as defender, William Troost Ekong bundled down Mandzukic in the box and influential midfielder, Luka Modric stepped up and took young goalkeeper, Francis Uzoho the wrong way to sealed up the game.
"Sometimes we were a little bit naive on set pieces but we will work on it".
"So many signs, the team have a real relationship with Russian Federation", said the Super Eagles' German coach Gernot Rohr. However, if the Eagles are to truly overachieve, he will need to give them free rein, and let the madness in.