Freshman Chanelle Price, who graduated from Easton High School and trains in Philadelphia with the United Stars Track Club, helped the Vols emerge from a three-team pack with an 800-meter leg of 2:04.5, and Bowman brought it home in the final 1,600 in 4:40.7.
Phoebe Wright (1,200 meters) and Kimarra McDonald (400), a graduate of Rancocas Valley High, ran the first two legs for Tennessee.
"It's always nice to get the baton in the lead," said Bowman, a senior. "But you have to hold it. I think I became a little too complacent through the middle of the race, but we held on to it and that's what counts. A victory is a victory."
Georgetown, with anchor Maggie Infeld quickly closing ground at the finish, crossed the line about 10 meters behind for second in 11:02.85. Villanova took third in 11:13.69 thanks to a strong anchor leg by Frances Koons.
The winning time was well off Villanova's 21-year-old Penn Relays record of 10:48.38, but Bowman said because of the swirling wind in the stadium, "It wasn't a day for records. It just wasn't happening."
Tennessee coach J.J. Clark, who competed at the Penn Relays in high school and in college at Villanova, said he didn't dwell on his team's disappointments here last year because of the gritty performances he saw on the track.
"Last year was a success, in my mind," Clark said. "They ran fast. They gave everything they had and put it on the line. So coming back this year and winning was exciting.
"I have to take my hat off to this team, because indoors there were high expectations and outdoors there are high expectations. To win time after time, it's very impressive, and they stand up to the test."