Butler (14-2, 3-1 Big East), which upended the defending national champions 66-58 on Wednesday, never trailed in the overtime to earn its third consecutive victory.
"After the Villanova game, we celebrated that night, but we knew we had to get back focused with Georgetown because we knew it would be a fight," said Baldwin, whose previous career-best was 14 points against Indiana on Dec. 17.
L.J. Peak scored 21 points and Jagan Mosely added a career-high 20 for the Hoyas (8-8, 0-4), who lost their first four conference games for the first time since 1998-99.
"We have to fight," Georgetown coach John Thompson III said. "It's as simple as that. There's no magic dust that can be sprinkled. We just have to come and fight."
Georgetown led by three points entering the final minute of regulation and had a chance to avoid overtime, but Peak's turnaround jumper at the buzzer clanked off the rim.
Pryor entered the day tied for the conference lead in scoring at 19.8 points per game, but was held scoreless on eight shots as Baldwin badgered him for much of his 24-minute stint.
But Butler also needed him at the offensive end to get past the struggling Hoyas.
"I thought he made some end-of-clock and play-after-the-play shots that were really critical for us," Bulldogs coach Chris Holtmann said. "Their size and length bothered us, stymied us at times. Our ball movement has to get better, but I thought when things broke down he made some critical plays."
The Hoyas did a solid job on Kelan Martin, who averaged 26.5 points in two games against Georgetown last season. Martin scored 13 points on 3-of-13 shooting and added 10 rebounds.
Butler stayed in the game thanks to its 10-of-20 showing from 3-point range. The Bulldogs shot just 39.1 percent from the field and were outscored 40-20 in the paint.
"It wasn't always like we wanted it to be, but much like it is on the road in most situations, you're going to have to weather some of that and I thought we weathered it and made the necessary plays," Holtmann said.
Butler: The Bulldogs remain entrenched in the top half of the Big East, impressively fending off a desperate Georgetown team to win their third straight against the Hoyas.
Georgetown: The Hoyas haven't won since before Christmas and along with DePaul remain one of two teams in the Big East without a conference victory.
Butler guard Kethan Savage is a Fairfax, Virginia native and played his first three college seasons at George Washington. In his first game back in the area since transferring he finished with 11 points, including the two free throws that gave the Bulldogs the lead for good in overtime.
Butler sophomore Nate Fowler played a career-high 19 minutes, scoring 11 points and grabbing four rebounds to fortify the Bulldogs' frontcourt. Fowler's 3-pointer with 54 seconds left in regulation tied it at 66, and his free throws with 8.5 seconds remaining secured a 68-68 tie to prompt overtime.
Butler was near-certain to rise in next week's rankings thanks to its victory over Villanova, but this ensures it. The Bulldogs have a good chance to move into the top 15 as a result of their 2-0 week.
Butler looks to add another victory over a ranked team when it visits No. 10 Creighton on Wednesday in the first of two regular-season meetings with the Bluejays.
Georgetown has a quick turnaround for its home date Monday against St. John's, which has lost its last 11 road games against the Hoyas.