The hosts wanted a penalty when Vaclav Kadlec was tripped in the box, but the referee ruled that there was no foul by the Augsburg defender.
Kadlec was involved again later in the first half as he tried to backheel the ball in from a Haris Seferovic ball into the box, but the winger's finish was inches wide.
After a dominant spell by Frankfurt, the visitors thought that they had opened the scoring against the run of play when Bobadilla sliced the ball home, but the assistant referee adjudged him offside.
Bobadilla did give Augsburg the lead early in the second half when the hosts failed to clear, allowing the midfielder to take on a first-time shot which bounced in off the inside of the left upright.
Frankfurt had a couple of half-chances as they tried to force an equaliser, with Seferovic heading wide before Alexander Meier saw his shot blocked.
Tobias Werner came close to putting the win beyond doubt for the visitors inside the final five minutes when he launch a powerful volley from the edge of the box, but his shot was kept out by the post.
However, Bobadilla's earlier effort proved enough for Augsburg to secure all three points to move up to 12th in the table, while Frankfurt sit 10th.