Third-placed Sweden host Moldova on Monday when Russia welcome Montenegro needing a point to claim a spot at the finals in France because they have a better head-to-head record.
It took Sweden 18 minutes to get a shot on target but when it came it put them ahead, Marcus Berg holding off the challenge of Liechtenstein captain Mario Frick before slotting home.
Sweden's all-time leading scorer Ibrahimovic won a penalty five minutes before halftime but goalkeeper Peter Jehle flung himself to his right to save the striker's spot kick.
Ibrahimovic made amends for that miss 10 minutes into the second half, latching on to Kim Kallstrom's long ball to rifle home his 58th international goal.
Berg and Ibrahimovic then both missed good chances as the sluggish Swedes failed to make the most of their dominance.
(Reporting by Philip O'Connor; editing by Ken Ferris)
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