The Bears defeated the previously unbeaten Gonzaga Bulldogs 86-70, with guard Jared Butler named MVP following 22 points, three rebounds and seven assists.
Baylor's first national title comes 18 years after the scandal which rocked the NCAA and led to Drew's appointment as coach to rebuild the team in 2003.
"I prayed about it," Drew said post-game. "God has blessed us with unbelievable players.
"Our fans who have been with us throughout the lean years [deserve this]. Our administration and the city of Waco deserves this. The state of Texas deserves it."
Baylor got a fast start, scoring the first nine points of the game and were never headed, leading by as many as 20 points in the last.
"All year long this is what they do," Drew said. "We have a starting rotation. Each night might be someone different but they've sacrificed all along.
"If you're going to be in a bubble for three to four weeks, you want do it with people you love. They're unbelievable basketball players, better people."
Gonzaga coach Mark Few admitted the Bears were simply too good.
"They just beat us in every facet of the game tonight," Few said. "Hats off to Baylor."
In doing so, FDU became the second 16-seed in tournament history to advance into the second round, joining the 2018 UMBC Retrievers.
Adding to the unlikeliness of their upset, the Knights are the shortest team in all of division one basketball this season – among 363 teams – and they had to deal with seven-foot-four National Player of the Year candidate Zach Edey.
Edey still had his way, scoring 21 points on seven-of-11 shooting while adding 15 rebounds and three blocks. He became the first player in tournament history to put up those numbers and still lose, dating back to when blocks became an official stat in 1986.
It was the only shocking upset of the day, although the six-seed Iowa State Cyclones were totally outmatched in their 59-41 defeat at the hands of the 11-seed Pittsburgh Panthers.
Despite a quiet game from the top NBA prospect in action Friday – Keyonte George – the three-seed Baylor Bears had no issue sending home the UC Santa Barbara Gauchos 74-56.
George, a six-foot-four freshman guard, is averaging 15.8 points, 4.2 rebounds and 2.8 assists as a starter on a quality outfit, but he had just nine points against the Gauchos as the Baylor starters got an early rest.
The most eye-catching individual performance of the day came from reigning National Player of the Year Oscar Tshiebwe, with the six-foot-nine senior piling up 25 rebounds in the six-seed Kentucky Wildcats' 61-53 triumph over the 11-seed Providence Friars.
Tshiebwe finished with 11 offensive rebounds to go with 14 on the defensive end, adding eight points, three steals and two blocks.
The other top seeds in action all survived and advanced, with two-seed Marquette beating 15-seed Vermont 78-61, three-seed Gonzaga getting the better of Grand Canyon 82-70, and three-seed Xavier surviving an early scare to overcome Kennesaw State 72-67.
Baylor, which boasts two likely first round picks in this year's NBA draft in Jeremy Sochan and Kendall Brown, looked dead in the water with 10 minutes to play, trailing 67-42.
From that point on it was like a scene from a movie, as the Bears could not miss, while the Tar Heels committed silly mistakes as the pressure mounted.
Trailing by six points with 35 seconds on the clock, Baylor's Sochan hit a three, before North Carolina missed both free throws, allowing James Akinjo to tie the game with a three-point play to force overtime.
Against all momentum, North Carolina steadied in the overtime period, winning it 13-6 to ultimately prevail 93-86.
