But on Tuesday, Iceland had few chances against an inspired Croatian team.
"Pressure was huge, this was not easy game to play," Croatia coach Niko Kovac said. "But at the end, it could have easily been 5-0."
Croatia took the lead when Ivan Rakitic crossed from the right, Ivan Perisic deflected the ball in the heart of the penalty box, creating a clear opportunity for Mandzukic to finish with a low shot into the near corner.
Bayern Munich striker Mandzukic was shown a straight red card after a tackle with his studs up against Johann Gudmundsson, and that changed Croatia's tactical approach for the rest of the game. With Iceland going into an all-out attack, Croatia resorted to counter-attacks.
Captain Srna doubled the lead two minutes into the second half when his shot from some 18 meters (yards) from the right bounced in front of Iceland goalkeeper Hannes Halldersson and ended up in the left corner of the goal.
"We were focused throughout the playoffs and it was worth it," Srna said. "We had no right to disappoint our fans. Mandzukic's sending off only gave us the wind in our backs."
Openings in Iceland's defense only created more chances for the Croats. Ivica Olic hit the crossbar with a spectacular overhead shot and Perisic failed to convert a one-on-one situation against the Iceland goalkeeper.
"We are really happy to make it to the World Cup," Croatia and Real Madrid midfielder Luka Modric said. "Iceland was tough to play against, but we were a better team in the playoffs."
Iceland was surprisingly unbeaten in its last five games on the road in these World Cup qualifications.
"Croatia was a better and more experienced opponent and showed its strength," Iceland veteran striker Eidur Gudjohnsen said. "Still, we have to be proud of what we have done in this World Cup campaign."
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Associated Press writer Igor Rajkovic contributed.