KNOXVILLE, Tenn.—Tennessee’s offense improved in a 35-3 win over UAB on Saturday. The Volunteers still need to improve some more, though.

Tennessee (1-1) erased bad memories of a poor offensive effort wrought with mistakes at UCLA two weeks ago against a Blazers defense that ranks as one of the worst in the Football Bowl Subdivision.

Three of the Vols’ next four opponents—No. 4 Florida, No. 9 Auburn and No. 2 Georgia—will pose a bit more of a challenge.

“It was a challenge to get our offensive team in a rhythm,” Tennessee coach Phillip Fulmer said. “We neede...

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