Harris, a freshman, was 11 of 14 from the foul line in surpassing his previous high of 21 set in his first Southeastern Conference game against Arkansas.
Hopson scored 16 of his points in the opening half as the Vols (18-12, 8-7) opened a 20-point lead.
The Gamecocks (14-14, 5-10) cut the margin to 69-66 with 1:06 to go. But Tennessee's Melvin Goins followed with a jumper and South Carolina could get no closer.
Senior Sam Muldrow had a career-high 24 points to lead the Gamecocks in his last regular-season game at Colonial Life Arena. Muldrow also collected 12 rebounds.
GEORGIA TECH 80, WAKE FOREST 54
In Winston-Salem, N.C., Iman Shumpert scored 24 points and Maurice Miller 20 as Georgia Tech routed Wake Forest.
Jason Morris added 13 points for the Yellow Jackets (12-17, 4-11 Atlantic Coast Conference), who pulled away from a seven-point halftime lead to snap an eight-game conference losing streak.
Gary Clark had 15 points, Travis McKie 11 and C.J. Harris 10 for the Demon Deacons (8-22, 1-14), who lost their ninth consecutive league game.
The loss also continued Wake Forest's season of frustration under first-year head coach Jeff Bzdelik, who replaced Dino Gaudio after three winning seasons and two trips to the NCAA Tournament.
Already assured of its worst record since 1985-86 -- going 8-21 in then-head coach Bob Staak's first season -- the Demon Deacons also posted their worst ACC record since 1986-87 (2-12).
NO. 10 WISCONSIN 77, INDIANA 67
In Bloomington, Ind., Jordan Taylor scored a career-high 39 points and almost single-handedly stopped Indiana's second-half charge, leading Wisconsin to victory.
With three of Wisconsin's starters in foul trouble, Taylor accounted for all the Badgers' points in a decisive 14-4 run midway through the second half. That spurt turned a 46-45 lead into a 60-49 advantage.
The Badgers (23-6, 13-4 Big Ten) have won eight in a row in the series.
SETON HALL 84,
NO. 15 ST. JOHN'S 70
In Newark, N.J., Jeremy Hazell scored a season-high 31 points and Seton Hall, the worst 3-point shooting team in the Big East, made a season-best 12 from beyond the arc in a victory over St. John's, snapping the Red Storm's six-game winning streak.
Freshman Fuquan Edwin had a career-best 19 points for the Pirates (12-17, 6-11), who had lost three in a row and five of six.
Dwight Hardy scored 23 points for St. John's (19-10, 11-6), which was one of the hottest teams in the country, having won eight of nine.
NO. 18 ARIZONA 70,
OREGON STATE 59
In Tucson, Ariz., Derrick Williams had 15 points and 12 rebounds, Lamont Jones added 17 points and Arizona moved a step closer to its first Pac-10 title in six years with a win over Oregon State (10-18, 5-12).
Coming off consecutive losses for the first time this season, Arizona (24-6, 13-4) pulled away in the second half to move within a game of its first undefeated home season in 12 years.