ZAGREB, Croatia -- Ten-man Croatia qualified for the World Cup with a 2-0 win on Tuesday that quashed Icelands hopes of reaching footballs showpiece tournament for the first time. Striker Dario Mandzukic scored the opener in the 22nd minute but was given a red card nine minutes later for a reckless tackle and left Croatia with 10 men for the remainder of the match. But the home team maintained its attacking dominance and Darijo Srna made it 2-0 in the 47th. The defeat ended Icelands bid to become the smallest nation -- in terms of population -- to reach the World Cup finals. Croatia, a semifinalist in 1998, qualified for its fourth World Cup since becoming an independent state in 1991. "Croatia deserved to win," Iceland defender Ragnar Sigurdsson said. "It was the better team, especially today, and there is no doubt it deserves to go to Brazil. We felt it might go better for us after Mandzukic was sent off, but we did not get any space on the pitch." Last Friday in Reykjavik, Iceland overcame the second-half red card of Olafur Skulason to hold on for the 0-0 draw against Croatia, keeping the Nordic nation in contention for a spot at Brazil in 2014. 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 Croatias 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 metres (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. Mandzukics sending off only gave us the wind in our backs." Openings in Icelands defence 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. 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