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Joel Campbell’s third-minute strike was enough for Los Ticos to secure qualification to their third consecutive World Cup appearance.
The former Arsenal striker scored after three minutes for Costa Rica as he squeezed between two defenders to touch home a square pass from Jewison Bennette with the New Zealand defence slow to react.
However, the match didn’t come without controversy with Kiwi striker Chris Wood’s equaliser chalked off by VAR for a foul in the build-up.
A check found that Matthew Garbett had fouled Oscar Duarte in what looked a harsh decision.
A VAR check also led to a 69th-minute red card for Kosta Barbarouses, leaving the Kiwis down to 10 men.
"We had a chance to score early on and then we struggled," said Costa Rica coach Luis Fernando at the post-match press conference.
"We knew what their assets were. We knew we’d struggle with their aerial balls. We had to make a change at halftime to have greater possession of the ball and a line of five in defence. That proved key."
The playoff between the fourth-placed team in the CONCACAF region and the Oceania confederation winner, at the Ahmad bin Ali Stadium, brought to an end the qualifying campaign for the 2022 finals in Qatar which kick off on November 21.
Costa Rica qualified for a sixth World Cup in total and will compete in Group E at the finals against Germany, Japan and Spain.
Campbell’s goal had some 6,000 travelling supporters, out of a crowd of 10,803, on their feet but did not precipitate the expected dominant performance from the central American team.
Instead, it was New Zealand who looked the more enterprising of the teams, with centre forward Wood, who was constantly watched by a cautious Costa Rican defence, the target of their attacks.
Alex Greive and Garbett also had chances in the first half but their shooting was off target.
Three changes by Costa Rica at halftime lifted them out of their slumber but it was still New Zealand who showed more attacking enterprise in the second half but without any return.
Costa Rica goalkeeper Kaylor Navas made a good stop in the 76th minute from Clayton Lewis as New Zealand toiled in search of an equaliser with Costa Rica sitting back and absorbing the pressure until the final whistle set off joyous celebrations.
"I thought we were by far the better team," said disappointed New Zealand coach Danny Hay.
"One team dominated, there was only one team trying to put together good quality football."