Baylor (5-1) never trailed after Brown scored eight points in an early 11-0 run.
"Bottom line, as I told them, we won. We won a championship. I don't care where you are, championships are hard to come by," Baylor coach Kim Mulkey said. "We're a team that carries Baylor across the chest, and we're not the same team we were as last year. But we're pretty darn good."
The only lead for Georgia Tech (6-1) was 3-2 after Lorela Cubaj hit a 3-pointer less than a minute into the game.
After the Lady Bears had five early turnovers against the pressing Yellow Jackets, Brown started the big run by making a jumper with 7:27 left in the first quarter. By time Cox made a jumper just more than 3 minutes later, they led 13-3.
"It was tough, very physical. Georgia Tech was a great team, great athleticism and they gave us a challenge," said Brown, who was named the tournament MVP. "I thought that what we lacked was the experience, so the press probably did startle us a little bit and it got us a little stagnant. In the timeout, coach made a few changes and we were able to break it."
Imani Tilford led Georgia Tech with 13 points, and Elo Edeferioka had 12 before fouling out.
Kristy Wallace added 12 points for the Lady Bears, and Alexis Morris had 11.
Mulkey expected the physical play from Georgia Tech, and the only thing that disappointed her was when Brown had three fouls before halftime.
"That's their style of play. ... I love that, but I want to be able to do it too. I don't want to have Kalani sitting over there by me," Mulkey said. "I thought we grew up a lot today. I thought Lauren Cox carried us, she and Kristy."
Georgia Tech: The Yellow Jackets had won their first six games, but facing a Top 10 team provided their first significant test.
Baylor: Mulkey's team got to have some fun with the day off Friday, with a beach day that included snorkeling into a shipwreck, jet skis and feeding stingrays. Back on the court, they won the Junkanoo Jam title for the third time. The Lady Bears now have a few days off before the most challenging part of their non-conference schedule.
Georgia Tech will be home against Purdue in the Big Ten/ACC Challenge on Thursday night.
Baylor hosts No. 22 Kentucky (5-0) on Thursday night in the Big 12/SEC Challenge, and three days after that the Bears play No. 14 Stanford in the Ferrell Center.
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