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The home side dominated their less illustrious opponents from the early stages, but the visitors were intent on defending stoutly, as Mikael Antonsson and Martin Olsson saw shots blocked by the Liechtenstein back line.
Emil Forsberg was next to threaten, the Malmo youngster bearing down on goal twice in the ninth minute, before Olsson tested the resolve of the away side's defence moments later.
Sweden kept dominating possession and plugging away on goal, eventually breaking the deadlock in the 34th minute when Zengin tucked the ball into the bottom corner of the net past Cengiz Bicer, much to the relief of the home crowd.
The Eskisehirspor man nearly doubled the lead with nine minutes left of the first half, but his free kick just missed the top left corner.
No sooner had the second half begun than Sweden doubled their lead, as Jimmy Durmaz struck home from the right-hand side of the Liechtenstein box with just 24 seconds on the clock.
Daniel Kaufmann then gave the visitors a rare chance in front on goal in the 71st minute, but the FC Vaduz man's effort was off target.
Ultimately, Sweden could not breach Liechtenstein's defence any more, and had to settle for a two-goal victory when they may have been expected to bump up their goal difference.