Tennessee (2-0) hasn't lost at home since falling 75-71 to Kentucky on Feb. 16, 2014.
Graves shot 8 of 8 from the floor and 8 of 8 from the free-throw line to help Tennessee survive a game that had nine ties and 12 lead changes. Mercedes Russell added 14 points and 13 rebounds.
Peyton Whitted had 17 points and 16 rebounds for Penn State (2-1). Her father, Kevin Whitted, played for the Tennessee men's team from 1992-95.
Penn State's Brianna Banks, who was averaging a team-high 21 points per game, played just two minutes. The Connecticut transfer's right leg was in a walking boot as she watched from the bench in the second half.
The Lady Vols pulled ahead for good with 4:55 remaining, breaking a 64-all tie on Diamond DeShields' putback of Te'a Cooper's missed 3-pointer. DeShields scored just four points and shot 2 of 11 in the North Carolina transfer's second game with Tennessee.
Tennessee had opened the season Sunday by beating Central Arkansas 102-47 despite playing only six people, as virtually half the roster was unavailable due to injuries and disciplinary matters. Tennessee coach Holly Warlick didn't specify Sunday which missing players were hurt and which were out for violating team rules.
The Lady Vols used 10 players Wednesday and needed the depth to survive a much tougher matchup. Graves, one of the players who didn't appear in the Central Arkansas game, made the difference by matching her career high in points.
Teniya Page scored 15 points, Lindsey Spann had 14 and Kaliyah Mitchell added 11 for Penn State. Mitchell scored all her points in the first half and she ended up fouling out with 7:23 remaining.
Penn State: Debbie Hawhee, who played on Tennessee's 1989 and 1991 national championship teams, now is a professor in Penn State's English department and a faculty partner for its women's basketball program.
Tennessee: Playing its first eight games at home this season before going to Wichita State on Dec. 11. Never before has Tennessee played more than six straight home games to open a season.
Penn State: Hosts Central Connecticut State on Sunday.
Tennessee: Hosts No. 25 Syracuse on Friday.