The contest was tied briefly at 2-2 in the game's first minute, but Tech (16-9, 7-7) heated up from behind the 3-point line and posted a 46-28 halftime lead.
Tech guards Amber Tarr and Natalie Ritchie combined for five 3-pointers in the first half.
Ritchie, who scored eight of her 13 points in the first half, said she simply followed Tarr's example.
"I just came in and tried to hit the open shots when I had them," Ritchie said. "It opened up for me, and I was glad I made them. But Amber started us off and that was great because she got the momentum going for us."
In addition to Ellison's double-double, Tech forward Jolee Ayers collected a double-double, scoring 14 points and grabbing 13 rebounds. Tech coach Marsha Sharp said Tuesday's play from the Lady Raider post players was their best effort this season.
"We played well on the inside against Kansas in the first game of conference play," Sharp said. "But possibly for 40 minutes, it (tonight) is probably the best we have gotten from the combination. They've each had good nights, but this is probably the best they have played together."
Ellison's 19-point effort was second only to A&M guard Toccara Williams' game-high 22 points.
Ellison, who entered the game averaging four points and four rebounds per game, said she adjusted early and then attacked A&M.
"I guess I was just in a zone," said Ellison. "I was just going with the flow. I wasn't really paying attention to how many points I was going to score. If I got the open shot, I took it. If one of my teammates was going to shoot it, I was going to try my best to get the board. I think I just had that mentality tonight that the ball was going to be mine."
Tarr finished with 15 points, while center Cisti Greenwalt poured in 11 points and guard Jia Perkins added 10 points.