The Bulldogs (23-9) will be seeking their sixth consecutive trip to the regional semifinals when they play the region's top seed, North Carolina, on Tuesday. The top-seeded Tar Heels dispatched 16th-seeded Bucknell 85-50 earlier Sunday.
Angel Robinson led the eighth-seeded Bulldogs with 17 points and 11 rebounds, and Houts and Megan Darrah each scored 13.
Houts, who also had 12 assists, was a perfect 9-for-9 at the line.
"When you hit the first couple, it helps your confidence more than missing the first two," said Houts, who also had four rebounds and just two turnovers. "After you make the first two, you have the confidence to just knock them down."
Humphrey finished with 12 points and 11 rebounds.
"I thought we did a really nice job on Tasha, and then she had a big basket, obviously, in crunch time," Iowa coach Lisa Bluder said.
The shot was the rare fadeaway that coach Andy Landers liked seeing her take.
"Sometimes I think players resort to that shot when they're desperate," said Landers, in his 29th season with the Bulldogs. "But that wasn't desperate. That decision was driven by the will to win. I knew it was in when it left her hand."
Kristi Smith led Iowa (21-11) with 17 points and Wendy Ausdemore had 16, but the Hawkeyes ran out of steam in a back-and-forth game. There were 11 lead changes in the second half.
Iowa led 31-25 at halftime, but Georgia opened the half on an 11-3 run to go ahead 36-34 with 14:08 to play. The Bulldogs didn't again lead by more than three until the final minute.
It was knotted for the sixth time when Humphrey, a four-time all-Southeastern Conference selection, made a baseline turnaround jumper from about 10 feet with 58 seconds to play. Then Houts, who played all 40 minutes, sealed it at the line.
"She had to do it," Bluder said. "You're on the floor for a reason and if Georgia was going to win the game, they had to make their free throws or it was going to be a big factor. They did a good job of getting the ball in to her as well."
Georgia will bring a 5-0 career mark against North Carolina into the second round.
Iowa, which shared the Big Ten regular season title with Ohio State, was outscored 12-4 at the free-throw line, and was outrebounded 43-32. Johanna Solverson, Iowa's third-leading scorer, missed 11 of 13 shots.
The game was delayed for several minutes with 14:18 to play when a cheerleader from Georgia had to be carried off the court after landing hard on her back. The cheerleader, identified as Christine Conley, was down for several minutes before she was placed on a backboard and wheeled away on a stretcher.