"I felt we needed to be impressive," Fulmer said after keeping starting quarterback Tee Martin in until late in the fourth quarter of a 37-13 victory over the Blazers.
Making a bid to become the nation's top-ranked team, the No. 2 Volunteers pushed their record to 8-0, their best start since 1956, as No. 1 Ohio State fell 28-24 to Michigan State.
It should clear the way for the Vols to ascend to the top of the polls and the Bowl Championship Series computer ranking.
"It's special to be considered among the top teams nationally," Fulmer said. "We have to handle it maturely if we get there."
The Vols didn't overwhelm Alabama-Birmingham (2-7) but led from start to finish, didn't have to punt and weren't seriously threatened.
"I don't think we played as well as we should have," said receiver Cedrick Wilson, who caught a 28-yard touchdown pass from Martin to put the Vols up 31-3 early in the second half. "We can't have turnovers against a good team."
The Vols fumbled three times, twice leading to Alabama-Birmingham field goals.
Running back Travis Stephens agreed with Wilson, but added, "A win is a win, no matter how much you win by. Against Arkansas, we have to step it up and play hard."
The Vols' victory sets up a Southeastern Conference battle of unbeatens next week when No. 11 Arkansas 8-0) comes to Neyland Stadium.
Alabama-Birmingham coach Watson Brown, who was 0-5 against the Vols as coach at Vanderbilt, was impressed.
"Our players, to a man, said that was the hardest they've ever been hit," Brown said. "They said Tennessee was the most physical team they've played this year. With their defense and kicking game, I don't know of anybody who could be any better."
Martin ran for one touchdown and threw for one and Jeff Hall kicked three field goals in a game in which the Vols set the tone early.
Starting from their 3 on their second series of the game, the Vols drove the length of the field in 10 plays, completing their longest drive of the season on Travis Henry's 18-yard run. Henry carried on six of the plays.
That put Tennessee up 10-3, and the Vols weren't threatened thereafter. The Vols rolled up 446 yards of offense to 292 for Alabama-Birmingham (2-7).
Henry ran for 104 yards on 17 carries and scored once, his second 100-yard game of the season. Stephens added 61 yards on 14 carries and also scored a touchdown.
Martin, though sacked three times, was 18-of-25 for 274 yards with one touchdown and no interceptions. Besides the touchdown pass to Wilson, Martin ran it in from the 1 in the second quarter.
Martin's favorite target, Peerless Price, caught six passes for 103 yards.
Tennessee rolled up 27 first downs to UAB's 15. Blazers quarterback Daniel Dixon was 7-of-18 for 71 yards.
The Blazers, in their third year of Division I-A play, lost their fourth homecoming game in as many weeks.
"We would have liked to put more points on the board, but the bottom line is we got the win," Hall said.
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