The Hoyas' Renee Tomlin, Amanda Kimbers, Chelsea Cox and Emily Infeld finished in 10:51.49, the fifth-fastest time in the 32-year history of the race, on a day when thunderstorms delayed most of the events at Franklin Field by roughly 90 minutes.
The Volunteers had achieved a rare sweep of the distance medley, the 4x800 and 4x1500 at the Penn Relays the last two years, while Villanova had won the NCAA indoor title in the distance medley relay just last month.
But the Wildcats were done in by a dropped baton, and Tennessee was close with Virginia and Georgetown until the final lap.
That's when Infeld, a junior from University Heights, Ohio, pulled away. She clocked an anchor split of 4:31.56 in the 1,600, the fastest of any competitor in the race.
"I kind of like being an underdog going into a race," Infeld said. "It takes some of the pressure off. I think it's fun to come out and surprise people. Everyone on my team did their job, and I just wanted to do mine, too."
Tomlin, a senior, ran a 3:19.81 leadoff split in the 1,200. Kimbers, a sophomore, followed with a 54.54 in the 400, and Cox - just a freshman - ran a 2:05.58 in the 800.
"This is something we talked about for several years now," said Chris Miltenberg, the Georgetown coach. "We've been kind of joking, 'Nobody even mentioned us.' We weren't invited to the Penn Relays press conference. We came out and surprised a lot of people."
Tennessee, which was trying to become the fourth team to win the college women's distance medley three years in a row, placed second in 10:56.20. Virginia was third in 10:57.13.
"I was thinking, 'Just go out hard and don't let them pass me,"' Cox said. "I just thought if I get the baton (ahead), we're there. I know Emily's going to bring it in."
Villanova, which has a record nine distance medley titles and was primed for its first since 2006, watched its chances slip away when Christie Verdier dropped the baton on the second leg shortly after getting it. The Wildcats wound up 13th in the 14-team race.
Arkansas junior Tina Sutej repeated as the college women's pole vault champion and set a Penn Relays record by clearing 14-7 1/4.
The native of Slovenia previously set the national collegiate record (14-10 3/4) at the SEC indoors, and the NCAA indoor meet record of 14-7 1/4. On Thursday, she easily shattered the previous Penn Relays record of 13-10 1/2, set two years ago by Rachel Laurent of LSU.
"Better conditions than last year," said Sutej, who competed after the rain had cleared. "I liked it better. I jumped higher than last year, then I went for my national record. I took two jumps at it but was too tired."
TCU junior Whitney Gipson set a Penn Relays and Franklin Field record in the college women's long jump with a distance of 21-11 1/2. Her mark, achieved on her third attempt, bettered the previous meet and stadium record of 21-10, set in 2003 by Elva Goulbourne of Auburn.
Gipson easily won Thursday's competition, which took place just before the thunderstorm, and Leah Eber of Purdue was a distant second at 20-2 1/2.
"It's a PR and I'm doing a lot better this year than I was last year," Gipson said.
Princeton's Emma Ruggerio won the college women's hammer throw at 186-2. Indiana's Faith Sherrill won the college women's shot put at 57-10 1/2, and Penn State's Karlee McQuillen captured the college women's javelin title with a throw of 158-4.
Richmond's Andrew Benford won the college men's 3,000-meter steeplechase in 8:48.94.