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Crompton surpassed his career high of 310 yards with a 10-yard pass to Denarius Moore on Tennessee's first drive of the second half.
He tied his career high of five touchdown passes on the next play with a 16-yard connection to Moore to make it 49-7 with 12:38 left in the third quarter.
Crompton finished 21-for-27 and no interceptions and was replaced by backup Nick Stephens halfway through the third quarter.
Tennessee (5-4) gave coach Lane Kiffin his first winning streak and dominated the game much as it's done the series. The Vols hold a 21-1 advantage against Memphis and have won all 12 meetings in Knoxville.
But the games between the state rivals often have been closer than the record indicates. Six of the 10 meetings between the two teams since 1991 have been decided by fewer than two touchdowns.
David Oku took the opening kickoff 69 yards, and Bryce Brown scored on a 1-yard run 2 minutes later. Memphis (2-7) could do nothing to catch up.
The Vols never punted with Crompton in the game, though they turned the ball over when they couldn't convert a fourth-and-2 at the Tigers' 29 and when Dennis Rogan muffed a punt return.
Memphis drove 93 yards in its 2-minute offense and scored on a 36-yard run by Marcus Hightower to cut Tennessee's lead to 35-7 with 58 seconds left in the half. The Vols responded with a 55-yard drive and Crompton's 1-yard touchdown run with 4 seconds on the clock.
The Tigers have been hampered with injuries this season, and it especially showed on defense. The Vols had their way passing nearly the entire game with wide-open routes.
Crompton, who until a few games ago was more likely to throw interceptions than touchdowns, had his selection of scoring targets in Moore, Gerald Jones, Luke Stocker, Quintin Hancock and Nu'Keese Richardson. Stephens also hit Moore for a TD.
Jones led the receiving corps with 97 yards on four catches.
Crompton was only 5 yards and a TD pass short of tying his previous career high at halftime. By the break, Tennessee had outgained Memphis 382 yards to 104 and had gained 11 more first downs.
Memphis entered the game with the 100th-ranked defense, giving up an average 416.5 yards. Tennessee finished with 566 yards.
The Vols rank 13th in the nation in defense, but were playing second- and third-string players by the time Curtis Steele scored on a 1-yard run and again on a 3-yard run in the middle of the third quarter. The scores cut Tennessee's margin to 49-21.
Steele finished with 144 yards on 21 carries in addition to the two touchdowns. Will Hudgens was 19 of 31 for 194 yards and an interception.
Tennessee's Eric Berry, the Southeastern Conference's career interception return leader, inched closer to the NCAA career record when he picked off Hudgens and returned the ball 7 yards. Berry has 494 career return yards, 5 yards shy of Florida State's Terrell Buckley.
