The victory keeps UConn (7-1, 3-0 Big East) in sole possession of first place in the Big East, and all but assures them of the first Top-25 ranking the program's history.
USF (6-2, 1-2), which was ranked No. 2 just two weeks ago, has lost two straight.
Dixon ran for 115 yards in a rainy first half, helping UConn build a 16-0 lead. He carried the ball 32 times and also caught three passes for 42 yards.
The Bulls came back in the second half and cut the lead to 19-15 in the fourth quarter, before a 20-yard Tony Ciaravino field goal with 5:19 gave UConn its final margin.
Grothe finished with 146 yards rushing on 25 carries. He also threw for 189 yards, but had two interceptions.
The first came on a deflected pass with 8:25 left in the first half that UConn linebacker Scott Lutrus grabbed and ran 23-yards for a touchdown to make it 16-0. It was Lutrus's fourth pick of the season, and the second he has brought back for a score.
It took the Bulls just 29 seconds to get into the end zone after the free kick. Grothe ran 53-yards on second down to the UConn 10, and kept the ball again on the next play for the score.
UConn made it 19-9 on a 27-yard field goal from Tony Ciaravino with 1:34 left in the third. The Bulls then answered with a 47-yarder from Delbert Alvarado with 12:48 to go, and a 27-yarder five minutes later.
USF was forced to settle for that field goal after a 2-yard touchdown run was called back on a holding penalty against receiver Cedric Hill, and a pass into the end zone that Hill dropped.
That was one of several missed scoring opportunities for the Bulls.
Grothe used up almost eight minutes in the third quarter driving from the USF 34 to the UConn 4, but Robert McClain picked off Grothe in the end zone on third-and-goal to end that threat.
UConn quarterback Tyler Lorenzen was 13-for-25 for 194 yards and a touchdown. He also threw one interception.
Dixon, though, was the star. The sophomore carried the ball eight times for 53 yards on the Huskies first drive, which ended with a 22-yard field goal.
Connecticut then drove 80 yards in 14 plays to take a 9-0 lead with just under 6 minutes left in the half. Lorenzen found tight end Steve Brouse, who had slipped behind the defense from 3-yards out. The Huskies muffed the extra point when the snap went high and a desperation pass by holder Desi Cullen was incomplete.
UConn, which completed the transition from Division I-AA in 2002, came into the game 0-10 against ranked opponents.
Fans poured onto the field after the victory, joining the players in a wild celebration, though the goal posts remained intact.
The win was Randy Edsall's 48th, and perhaps biggest, in his 100 games as UConn's head coach.