Jenny Moshak got Graves to her feet and safely to the end of the bench, where she worked on the freshman's neck.
Some 83 seconds later, Graves was on the free throw line with Tennessee down by a point and 29 seconds left on the clock.
Graves had driven to the rim, but the shot didn't fall. Instead she had to pick herself off the floor and get to the line. She missed the first but appeared utterly calm. She focused on the rim to drain the second and tie the game at 70.
"I was very determined," Graves said. "I actually wanted that layup instead of shooting free throws."
Graves was back on the line in overtime with Tennessee ahead by one point, 76-75, and eight seconds left on the clock.
Graves drained both of those shots for the final 78-75 win over an athletic and determined Florida team.
Tennessee (13-3, 4-0) kept its conference slate clean against Florida (13-5, 2-2) in a tough venue to play because the huge facility also houses basketball practice and volleyball courts and a swimming pool, which keeps the air humid.
The Tennessee players were drenched during the game and also logged extensive minutes with Meighan Simmons checking in at 44 and Ariel Massengale at 42. Graves logged 38, a tremendous amount for a freshman playing for the first time at the McConnell Center.
Graves had to stay on the court because sophomore Isabelle Harrison got in early foul trouble - she was on the bench 78 seconds into the game and remained there until the start of the second half.
Harrison was called for a charge and then didn't fall back out of a trap at the top of the floor for foul number two.
"We talked about when we trapped the ball if they got under us to let them go," coach Holly Warlick said. "She can't put us in that situation."
That meant Graves had to handle the paint with the sophomore sidekick that keeps her calm and helps on the boards.
"Izzy is a big part of our game," Graves said. "It took out a big hole in our offense. It was a lot harder."
As usual, Graves delivered.
She had seven points, five boards, three assists and two steals to help Tennessee claim a 37-34 lead at halftime. She finished with 17 points on 6-11 shooting and 12 boards, none bigger than the final one she grabbed in overtime that sent her to the line after she was fouled.
"She was huge," Warlick said. "She's our workhouse."
Warlick's breath had to catch when Graves went down. The head coach already has two players keeping her company on the sideline in Andraya Carter, who is out for the season, and Cierra Burdick, whose broken right hand is healing well and is on track for a early February return.
"I knew when she caught her breath she would be alright," Warlick said.
Such is the faith the coaching staff has in Graves. It is extended to Simmons, whose 17 first-half points carried Tennessee when Harrison had to sit.
"She was huge," said Massengale, who tallied 12 points and four assists. "Meighan Simmons is one of the best I've seen in college basketball in the open court."
Twice Florida scored, and Simmons beat everyone down the court for layups.
"We knew she was going to come in here and try to get a lot of transition points," Florida's Carlie Needles said. "She is a playmaker. She makes some great plays."
Simmons finished with 27 points on 11-23 shooting overall and 4-9 from long range.
"Every time Meighan shoots and touches the ball we think it's going in," Warlick said.
Simmons, and Tennessee, started out scorching the nets. Simmons was 7-12 in the first half.
But the pace of the game and the temperature in the building wore on both teams - Tennessee would shoot 39.4 percent for the game, Florida, 43.2 percent - and as the shots began to not fall, the Lady Vols needed defensive stops.
That is where Warlick was well less than pleased.
"I was concerned by our lack of defensive intensity," Warlick said. " We looked disinterested on the defensive end."
Warlick mixed up defenses between man and zone and also pressed.
"I tried everything," Warlick said. "But they were still able to go to the rim."
The Lady Vols did get the stop they needed at the end of regulation. Jaterra Bonds drove left with Williams sticking to her. The screen didn't come and Bonds lost the handle on the ball and tried to toss it towards the rim.
"I tried to put it up and make some kind of contact," Bonds said.
Harrison, who finished with 10 points and nine boards, got Tennessee ahead on a layup to open the overtime period, but Florida led by two, 75-73, with 1:23 left on a Bonds' layup. Simmons answered with a bank shot to tie the game at 75.
Tennessee had possession with 24 seconds left when coach Amanda Butler made the decision to foul Williams in the backcourt and put her on the line for a one-and-one.
The decision backfired when the senior connected on the front end and made one of two.
"It was a calculated risk," Butler said. "It was a bad decision. It was tough to stop them one on one. If I had to do it over again I would trust our defense."
Tennessee had squandered opportunities at the rim late in the second half and in the overtime. The gamble almost worked but Christin Mercer, who was fouled, had her shot rattle out. When she missed both free throws, Graves got the rebound and sealed the game at the line.
Florida had to compete in the second half without its best player in Jennifer George, who re-injured her right shoulder before halftime while trying to get a rebound and will be evaluated Monday.
"That's going to give our team some confidence," Butler said. "We showed our balance is legit."
Florida dominated the bench scoring, 33-3.
"I thought our bench played a great game," Butler said. "We don't have subs. We bring another wave of attack."
The Gators also won the battle of the boards, 48-41.
"We haven't been out-rebounded in a long time," Warlick said.
Butler noted Tennessee was the best rebounding team in the SEC and one of the best in the country and had she known her team would win the glass with George limited to 12 minutes, "I would have felt this press conference would be me with a much better attitude," Butler joked.
Butler was proud of her team and she sounded as if observers weren't fully aware of how good the Gators could be.
"We didn't come out here for a good showing," Butler said. "I think we're one of the best teams in the country."
Warlick didn't like the board stats or the defensive lapses, but she was thrilled with the final numbers on the scoreboard.
"Are you kidding? Absolutely," Warlick said. "I love this team. They are just extremely, extremely coachable.
"It's a special group. They're not a selfish group. It's a special group for us."
The game kicked off the "We Back Pat" initiative and Butler wore a purple blouse and her players wore special T-shirts to support Pat Summitt and Alzheimer's awareness.
Butler was asked if it was odd to play Tennessee without Summitt on the sideline.
"I didn't think about it at all and that's a credit to Holly," Butler said. "People asked me before the game, ‘How is Tennessee different without Pat?' They're not different at all. Tennessee defense and Tennessee pride."
Ariel Massengale, Meighan Simmons, Bashaara Graves
Florida press conference