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Zlatan screamer beats holders
Ibrahimovic: Wonderful second half goal
The Inter Milan striker ended an international goal drought lasting over two-and-a-half years mid-way through the second half with a rasping drive to bring to life a dour encounter in Salzburg.
Peter Hansson doubled the Swedes' lead soon after with a messy goal that sealed victory over a negative and uninspiring Greece side.
The tone for a scrappy game was set in the opening two minutes when Angelos Charisteas was booked for a lunge on Hansson but it was Charisteas who had the first shot of the game, a low drive straight at Andreas Isaksson after a fine jinking run on seven minutes.
Anders Svensson saw a left-footed volley from outside the box flash just wide after 11 minutes as Sweden claimed the ascendancy and their best chance fell to Ibrahimovic as the half-hour mark approached.
West Ham's Freddie Ljungberg delivered a cross from deep on the left but Ibrahimovic could only flick his header onto the roof of the net with keeper Antonis Nikopolidis in no man's land.
The Greeks' contentment to keep the ball at the back drew cries of derision from the crowd but on one of the rare occasions they got men forward, Angelos Basinas drew a fine save out of Isaksson, who was forced to turn the Mallorca midfielder's long range shot around the post a minute before the break.
Sweden began the second half brightly and Christian Wilhelmsson had a wonderful opportunity to open the scoring three minutes after the interval but the Bolton flop lifted his lob over the bar from the corner of the penalty area with Nikopolidis again out of his goal.
Hansson nearly turned a Traianos Dellas cross into his own net but on 67 minutes, Ibrahimovic put the Swedes in front with a goal-of-the-tournament contender.
Collecting a throw-in on the right, the Swedish player-of-the-year played a neat one-two with Henrik Larsson before unleashing a wonderful 20-yard drive across Nikopolidis into the far top corner.
If the Swedes' first goal was sublime, the second was ridiculous.
Ljungberg found himself one-on-one with Nikopolidis in the 72nd minute but it was the Olympiakos keeper who came out on top, blocking the ex-Arsenal star's effort. The ball however looped up into the air towards the net and was bundled home by the knee of Hansson, despite the efforts of Nikopolidis and two of his defenders.
Isaksson was forced to block Vassilis Torosidis' shot from a tight angle with five minutes left, but Greece rarely threatened and now must take three points from their clash with Spain on Saturday to stay in the tournament.
Sweden however go into their clash with Russia knowing that a win will almost certainly send them through to the quarter-finals.