The Vols, with Sarah Bowman running a sizzling anchor leg, crossed the line in 17 minutes, 8.34 seconds, better than the mark of 17:09.75 set by an Australian team in 2000.
Villanova won a Championship of America relay for the first time since capturing the DMR in 2001. The last four years, the Cats had finished fifth, eighth, second and third, knocking on the door but failing to break through.
This year, however, they had the answer in the tall, long-striding Gibney, 20, who was a medical school student in Australia when he was recommended to Villanova coach Marcus O'Sullivan by a friend with whom he used to run professionally.
Oh, by the way, Gibney never had heard of the Penn Relays before coming to the Main Line.
"When I was getting recruited, it came up again and again," Gibney said. "The last couple of months, I got a sense of how important it is. The first time I spoke to Marcus at the start of the season, he said, 'If you run a good mile at Penn Relays and do nothing else the rest of the season, I'll be happy.'
"Just the last week, people who lived in Philadelphia all their lives said, 'I can't explain to you how big it is. You have to be there to see what a big thing it is to Villanova.' In terms of the atmosphere, I haven't been in anything near this before."
Gibney's teammates - seniors Sean Tully (1,200-meter leg) and Elvis Lewis (400) and sophomore Jason Apwah (800) - combined to get Gibney the baton in second place, three meters behind Ulrey, who had anchored Arkansas in its narrow second-place finish at last month's NCAA indoor championships.