The lone goal came from Anthony Partipilo in the 19th minute, who was found alone in the box by Antonio Palumbo thanks to a clever dummy by Mamadou Coulibaly.
Bari came close to equalising through Walid Cheddira, however the Moroccan international’s shot was just wide.
The visitors struggled to create any clear-cut opportunities, resorting instead to long-range efforts that barely troubled Antony Iannarilli in goal.
Ternana are three points outside the play-offs, while Bari are six points off automatic promotion.
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