Television replays showed the game clock seemed to pause as Anosike came down with the ball and two-tenths remained on the clock, leading to the controversial finish.
Anosike camly stepped up and hit the two free throws to seal the victory.
"It's unfortunate that those kinds of things happen," Rutgers coach C. Vivian Stringer said. "I'm getting used to it now."
Candace Parker, who bruised her knee in the Lady Vols' last game, had 27 points and 10 rebounds, and Angie Bjorklund added 13.
Epiphanny Prince had 21 points for Rutgers, and Essence Carson added 18.
The Lady Vols (22-1) entered the second half with a 34-23 lead after the Scarlet Knights (19-4) made only two field goals and two free throws in the 11 minutes before the half.
The deficit was Rutgers' largest of the season. They had trailed by 10 to both Connecticut and Maryland before coming back to win both games.
Tennessee coach Pat Summitt warned her team at halftime that it could happen again.
"Rutgers is a second half team, all you have to do is look at all their comebacks this year," she said.
But Tennessee went cold after the break, making only one shot from the field - a 3-pointer from Angie Bjorklund - in the first 14:30 minutes.
Rutgers took a 39-38 lead on a Rashidat Junaid layup with 10:08 to go. Vaughn's putback basket put the Scarlet Knights up 56-51 with 1:35.
Coming off a timeout, Shannon Bobbitt nailed a 3-pointer for Tennessee with 1:23 left. After Matee Ajavon missed a layup on the other end, Alexis Hornbuckle grabbed the rebound, setting up another 3-pointer by Bjorklund to put the Lady Vols up by 1.
Carson responded immediately with jumper with 26 seconds left. Bobbitt and Parker both missed shots on the goal before Anosike was fouled trying to grab the rebound.
Rutgers was coming off an 73-71 upset of previous No. 1 Connecticut and was trying to become the first team to ever beat No. 1 teams in consecutive games.
It was the first time in history the Scarlet Knights have played four ranked opponents in a row, having also faced No. 18 Pittsburgh and No. 11 West Virginia.
It wasn't the first time this season Rutgers lost a game on a controversial call at the end. The Scarlet Knights were beaten by Stanford on two free throws by Candice Wiggins with one-tenth of a second left when she was fouled by Prince 80 feet from the basket.
Tennessee shot only 29.6 percent from the field - the first time this season it has shot below 40 percent.
The Lady Vols shot a perfect 12-for-12 from the free throw line in the first half, but went 11-for-18 from the line in the second half for an unusually low 61.1 percent.
