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Dimtris Salpingidis of Greece, left, celebrates after scoring against Ukraine as teammate Giorgos Karagounis follows him on Wednesday. (Thanassis Stavrakis/Associated Press)

Greece is back in the World Cup for the first time in 16 years.

The 2004 European champions shocked the Donetsk crowd in Ukraine during the second leg of their World Cup qualifying playoff on Wednesday, winning 1-0 in the match and on aggregate to book a ticket to South Africa in 2010.

Greece striker Dimitrios Salpingidis scored the winner in the 32nd minute, sliding the ball past keeper Andrei Pyatov after he found himself free and clear, thanks to a Georgios Samaras pass from midfield that knifed through the Ukrainian defence.

"This is a huge win and we’re celebrating it," Salpigidis said. "We’ve heard a lot of criticism during the qualifiers and this is an answer to our critics. We never stopped believing in ourselves and we’ve made it."

Ukraine will rue its numerous squandered chances, as a combination of missed attempts on goal, tight Greek defending and solid goalkeeping by Alexandros Tzorvas kept Greece in front.

Ukrainian captain Andriy Shevchenko was especially snake-bitten. The former Serie A star missed several big opportunities to open Ukraine's account throughout the game.

At 33 years old, this might've been Shevchenko's last chance to reach the World Cup, and he was seen holding his head in his hands after the final whistle blew.

Ukraine's one and only appearance in the World Cup was in Germany in 2006, when Shevchenko carried his squad to the quarter-finals of the tournament.

Greece will appear in only its second World Cup, the last being in 1994 in the U.S., where it lost all three games and was eliminated in the group stage.

"I’m pleased for the guys," coach Otto Rehhagel said. "I told them no hill was too high, and they played with passion and commitment.

"Ukraine played a very good game. We weren’t able to break up Ukraine’s game as well as we hoped, but we hit them once on the break."

Many predicted a Ukrainian victory Wednesday after the two sides drew 0-0 in Athens on Saturday in the first leg of the European playoff, and the home side came out with a purpose in the opening phase of the game.

Shevchenko missed his first two chances to score seven minutes into the game.

The Dynamo Kiev striker first flubbed a left-footed shot while wide open in the box, and then skied a rebound over the bar with the net gaping after Greek keeper Tzorvas spilled Oleksandr Aliyev's hard shot.

Greece warned the Ukrainians of its dangerous counterattack when Samaras missed a dangerous header high off a free kick in the 10th minute.

Tzorvas was called on again to make another big save in the 17th when he parried Aliyev's hard free kick away from goal with a diving save.

One minute later, Greece's Salpingidis rushed his first attempt on goal wide after he found himself clear in the Ukrainian box. 

Salpingidis didn't miss on his second try though, giving Greece a 1-0 lead in the 32nd minute.

The goal meant that Ukraine needed to win the game outright, as a draw would be enough to see the Greeks through, as per the away goals rule in the two-game playoff.

Shevchenko missed yet another glorious chance to score three minutes away from halftime, along with Tymoschuk. While wide open only a couple yards away from the Greek net, both players completely missed the ball off a dangerous free kick and it was cleared from danger.

Boos rained down on the Ukrainians from the 31,100 fans at Olympic Stadium, which was almost 20,000 less than capacity.

"It is very painful for me that it has ended this way as I felt we deserved to qualify for the World Cup," Ukraine coach Oleksiy Mykhailychenko said. "It’s a shame we didn’t have quite enough skill and creativity. I don’t have any complaints about our players, they gave everything they had but it wasn’t enough."

Two more shots were parried away by Tzorvas in the 54th and 58th minute, one from Aliyev on a free kick and another from Shevchenko, both outside the box.

In the 60th, Ukraine substitute Yevhen Seleznyov just scraped the right corner with a first-time strike in the box.

Yaroslav Rakytskiy gave Tzorvas some more light work with a low dribbler in the 67th.

After that the Ukraine attack slowed. Oleg Gusev had a chance in close to give Ukraine some consolation near injury time but his sliding kick went high over the bar.

with files from The Associated Press